The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography （CT）, which creates the possibility for dose reduction. In this paper, a filtered-bac...The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography （CT）, which creates the possibility for dose reduction. In this paper, a filtered-backprojection （FBP） algorithm based on the Radon inversion transform is presented to deal with the three-dimensional （3D） local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography （ATRACT）, not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.展开更多
Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Usin...Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.展开更多
By combined power evolution laws of the spectral parameter and the initial constants of integration,a new differential-difference hierarchy is presented from the Toda spectral problem.The hierarchy contains the classi...By combined power evolution laws of the spectral parameter and the initial constants of integration,a new differential-difference hierarchy is presented from the Toda spectral problem.The hierarchy contains the classic Toda lattice equation,the nonisospectral Toda lattice equation and the mixed Toda lattice equation as reduced cases.The evolution of the scattering data in the inverse scattering transform is analyzed in detail and exact soliton solutions are computed through the corresponding inverse scattering transform.展开更多
Since its inception in the 1970s,multi-dimensional magnetic resonance(MR)has emerged as a powerful tool for non-invasive investigations of structures and molecular interactions.MR spectroscopy beyond one dimension all...Since its inception in the 1970s,multi-dimensional magnetic resonance(MR)has emerged as a powerful tool for non-invasive investigations of structures and molecular interactions.MR spectroscopy beyond one dimension allows the study of the correlation,exchange processes,and separation of overlapping spectral information.The multi-dimensional concept has been re-implemented over the last two decades to explore molecular motion and spin dynamics in porous media.Apart from Fourier transform,methods have been developed for processing the multi-dimensional time-domain data,identifying the fluid components,and estimating pore surface permeability via joint relaxation and diffusion spectra.Through the resolution of spectroscopic signals with spatial encoding gradients,multi-dimensional MR imaging has been widely used to investigate the microscopic environment of living tissues and distinguish diseases.Signals in each voxel are usually expressed as multi-exponential decay,representing microstructures or environments along multiple pore scales.The separation of contributions from different environments is a common ill-posed problem,which can be resolved numerically.Moreover,the inversion methods and experimental parameters determine the resolution of multi-dimensional spectra.This paper reviews the algorithms that have been proposed to process multidimensional MR datasets in different scenarios.Detailed information at the microscopic level,such as tissue components,fluid types and food structures in multi-disciplinary sciences,could be revealed through multi-dimensional MR.展开更多
The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus...The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus transform, Co is the cosines transform of Fourier and L is the Laplace transform.展开更多
The(2+1)-dimensional integrable generalization of the Kaup-Kuper-shmidt(KK)equation is solved by the inverse spectral transform method in this paper.Several new long derivative operators V_(x),V_(y) and V_(t) and the ...The(2+1)-dimensional integrable generalization of the Kaup-Kuper-shmidt(KK)equation is solved by the inverse spectral transform method in this paper.Several new long derivative operators V_(x),V_(y) and V_(t) and the kernel functions K of ■-problem are introduced to construct a type of general solution of the KK equation.Based on these,several classes of the new exact solutions,with constant asymptotic values at infinity u|_(x^(2)+y^(2)→∞)→0,for the KK equation are constructed via the-dressing method.展开更多
In this paper,we present some properties of scattering data for the derivative nonlinear Schrödinger equation in H^(S)(R)(s≥1/2)starting from the Lax pair.We show that the reciprocal of the transmission coeffici...In this paper,we present some properties of scattering data for the derivative nonlinear Schrödinger equation in H^(S)(R)(s≥1/2)starting from the Lax pair.We show that the reciprocal of the transmission coefficient can be expressed as the sum of some iterative integrals,and its logarithm can be written as the sum of some connected iterative integrals.We provide the asymptotic properties of the first few iterative integrals of the reciprocal of the transmission coefficient.Moreover,we provide some regularity properties of the reciprocal of the transmission coefficient related to scattering data in H^(S)(R).展开更多
The process and characteristics of loading on high-speed railway bridge pile foundation were firstly obtained by means of field research and analysis,and the corresponding loading function was presented.One-dimensiona...The process and characteristics of loading on high-speed railway bridge pile foundation were firstly obtained by means of field research and analysis,and the corresponding loading function was presented.One-dimensional consolidation equation of elastic multilayered soils was then established with single drainage or double drainages under multilevel loading.Moreover,the formulas for calculating effective stress and settlement were derived from the Laplace numerical inversion transform.The three-dimensional composite analysis method of bridge pile group was improved,where the actual load conditions of pile foundation could be simulated,and the consolidation characteristics of soil layers beneath pile were also taken into account.Eventually,a corresponding program named LTPGS was developed to improve the calculation efficiency.The comparison between long-term settlement obtained from the proposed method and the in-situ measurements of pile foundation was illustrated,and a close agreement is obtained.The error between computed and measured results is less than 1 mm,and it gradually reduces with time.It is shown that the proposed method can effectively simulate the long-term settlement of pile foundation and program LTPGS can provide a reliable estimation.展开更多
Based on a newly revised inverse scattering transform for the derivative nonlinear SchrSdinger （DNLS＋） equation with nonvanishing boundary condition （NVBC）, the explicit breather- type and pure N-soliton solution...Based on a newly revised inverse scattering transform for the derivative nonlinear SchrSdinger （DNLS＋） equation with nonvanishing boundary condition （NVBC）, the explicit breather- type and pure N-soliton solution has been derived by some algebra techniques. The two-breather solution and the pure double-soliton solution have been given as two typical examples in illustration of the general formula of the multi-soliton solution. The asymptotic behaviors of the N-soliton solution are discussed in detail.展开更多
Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harm...Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.展开更多
A newly revised inverse scattering transform（IST） is used to solve the derivative nonlinear Schr？dinger（DNLS-＋） equation with non-vanishing boundary condition（NVBC） and normal group-velocity dispersion, and a ...A newly revised inverse scattering transform（IST） is used to solve the derivative nonlinear Schr？dinger（DNLS-＋） equation with non-vanishing boundary condition（NVBC） and normal group-velocity dispersion, and a mixed type of soliton solution is found, which is composed of both pure and breather-type solitons. The mixed-soliton solution can degenerate into breathers and pure solitons when taking the limit of some special parameters, proving the validity of the mixed-type solution.展开更多
A newly revised inverse scattering transform（IST） for the derivative nonlinear Schrdinger（DNLS＋） equation with non-vanishing boundary condition（NVBC） and normal group velocity dispersion is proposed by introduc...A newly revised inverse scattering transform（IST） for the derivative nonlinear Schrdinger（DNLS＋） equation with non-vanishing boundary condition（NVBC） and normal group velocity dispersion is proposed by introducing a suitable affine parameter in Zakharov-Shabat integral kern.The explicit breather-type one-soliton solution,which can reproduce one pure soliton at the de-generate case and one bright soliton solution at the limit of van-ishing boundary,has been derived to verify the validity of the revised IST.展开更多
One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equatio...One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.展开更多
N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources andthe hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse sca...N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources andthe hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scatteringtransform.展开更多
In this paper,a time-frequency associated multiple signal classification(MUSIC)al-gorithm which is suitable for through-wall detection is proposed.The technology of detecting hu-man targets by through-wall radar can b...In this paper,a time-frequency associated multiple signal classification(MUSIC)al-gorithm which is suitable for through-wall detection is proposed.The technology of detecting hu-man targets by through-wall radar can be used to monitor the status and the location information of human targets behind the wall.However,the detection is out of order when classical MUSIC al-gorithm is applied to estimate the direction of arrival.In order to solve the problem,a time-fre-quency associated MUSIC algorithm suitable for through-wall detection and based on S-band stepped frequency continuous wave(SFCW)radar is researched.By associating inverse fast Fouri-er transform(IFFT)algorithm with MUSIC algorithm,the power enhancement of the target sig-nal is completed according to the distance calculation results in the time domain.Then convert the signal to the frequency domain for direction of arrival(DOA)estimation.The simulations of two-dimensional human target detection in free space and the processing of measured data are com-pleted.By comparing the processing results of the two algorithms on the measured data,accuracy of DOA estimation of proposed algorithm is more than 75%,which is 50%higher than classical MUSIC algorithm.It is verified that the distance and angle of human target can be effectively de-tected via proposed algorithm.展开更多
The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokho...The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.展开更多
The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–...The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. Then the Riemann–Hilbert problem corresponding to the reflection-less case is solved.As applications, multi-soliton solutions are obtained for the coupled Sasa–Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons.展开更多
N-lump solutions of the Kadomtsev-Petviashvili I equation in non-uniform media are derived through the inverse scattering transform. The obtained solutions describe lump waves with time-dependent amplitudes and veloci...N-lump solutions of the Kadomtsev-Petviashvili I equation in non-uniform media are derived through the inverse scattering transform. The obtained solutions describe lump waves with time-dependent amplitudes and velocities. Dynamics of l-lump wave and interactions of two lump wave are illustrated.展开更多
Since the Jost solutions of the DNLS equation does not tend to the free Jost solutioins as ｜λ｜→∞, the usual inverse scattering transform （IST） must be revised. Beside the Kaup and Newell＇s approach, we propose...Since the Jost solutions of the DNLS equation does not tend to the free Jost solutioins as ｜λ｜→∞, the usual inverse scattering transform （IST） must be revised. Beside the Kaup and Newell＇s approach, we propose a simple revision in constructing the equations of IST, where the usual Zakharov-Shabat kern is revised by multiplying λ^-2 or λ^-1. To justify the revision we show that the Jost solutions obtained do satisfy the pair of compatibility equations.展开更多
In the present paper the Riesz fractional coupled Schr6dinger-Boussinesq （S-B） equations have been solved by the time-splitting Fourier spectral （TSFS） method. This proposed technique is utilized for discretizing ...In the present paper the Riesz fractional coupled Schr6dinger-Boussinesq （S-B） equations have been solved by the time-splitting Fourier spectral （TSFS） method. This proposed technique is utilized for discretizing the Schrodinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.展开更多
基金Project supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603)
文摘The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography （CT）, which creates the possibility for dose reduction. In this paper, a filtered-backprojection （FBP） algorithm based on the Radon inversion transform is presented to deal with the three-dimensional （3D） local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography （ATRACT）, not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.
基金Supported by the Foundation of the National Natural Science of China( No.1 0 0 71 0 39) and the Foundation of Edu-cation Commission of Jiangsu Province
文摘Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671177,11771186)Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX212566)。
文摘By combined power evolution laws of the spectral parameter and the initial constants of integration,a new differential-difference hierarchy is presented from the Toda spectral problem.The hierarchy contains the classic Toda lattice equation,the nonisospectral Toda lattice equation and the mixed Toda lattice equation as reduced cases.The evolution of the scattering data in the inverse scattering transform is analyzed in detail and exact soliton solutions are computed through the corresponding inverse scattering transform.
基金supported by the National Natural Science Foundation of China(No.61901465,82222032,82172050).
文摘Since its inception in the 1970s,multi-dimensional magnetic resonance(MR)has emerged as a powerful tool for non-invasive investigations of structures and molecular interactions.MR spectroscopy beyond one dimension allows the study of the correlation,exchange processes,and separation of overlapping spectral information.The multi-dimensional concept has been re-implemented over the last two decades to explore molecular motion and spin dynamics in porous media.Apart from Fourier transform,methods have been developed for processing the multi-dimensional time-domain data,identifying the fluid components,and estimating pore surface permeability via joint relaxation and diffusion spectra.Through the resolution of spectroscopic signals with spatial encoding gradients,multi-dimensional MR imaging has been widely used to investigate the microscopic environment of living tissues and distinguish diseases.Signals in each voxel are usually expressed as multi-exponential decay,representing microstructures or environments along multiple pore scales.The separation of contributions from different environments is a common ill-posed problem,which can be resolved numerically.Moreover,the inversion methods and experimental parameters determine the resolution of multi-dimensional spectra.This paper reviews the algorithms that have been proposed to process multidimensional MR datasets in different scenarios.Detailed information at the microscopic level,such as tissue components,fluid types and food structures in multi-disciplinary sciences,could be revealed through multi-dimensional MR.
文摘The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus transform, Co is the cosines transform of Fourier and L is the Laplace transform.
基金supported by the National Natural Science Foundation of China(Grant Nos.12371256,11971475).
文摘The(2+1)-dimensional integrable generalization of the Kaup-Kuper-shmidt(KK)equation is solved by the inverse spectral transform method in this paper.Several new long derivative operators V_(x),V_(y) and V_(t) and the kernel functions K of ■-problem are introduced to construct a type of general solution of the KK equation.Based on these,several classes of the new exact solutions,with constant asymptotic values at infinity u|_(x^(2)+y^(2)→∞)→0,for the KK equation are constructed via the-dressing method.
基金W.W.was supported by the China Postdoctoral Science Foundation(Grant No.2023M741992)Z.Y.was supported by the National Natural Science Foundation of China(Grant No.11925108).
文摘In this paper,we present some properties of scattering data for the derivative nonlinear Schrödinger equation in H^(S)(R)(s≥1/2)starting from the Lax pair.We show that the reciprocal of the transmission coefficient can be expressed as the sum of some iterative integrals,and its logarithm can be written as the sum of some connected iterative integrals.We provide the asymptotic properties of the first few iterative integrals of the reciprocal of the transmission coefficient.Moreover,we provide some regularity properties of the reciprocal of the transmission coefficient related to scattering data in H^(S)(R).
基金Project(2012QNZT050)supported by the Special Fund for Basic Scientific Research of Central Colleges,ChinaProjects(51208518,U1361204,51208519,51108464)supported by the National Natural Science Foundation of China+1 种基金Project supported by the Postdoctoral Foundation of Central South University,ChinaProjects(2013RS4030,2012RS4002)sponsored by Hunan Postdoctoral Scientific Program,China
文摘The process and characteristics of loading on high-speed railway bridge pile foundation were firstly obtained by means of field research and analysis,and the corresponding loading function was presented.One-dimensional consolidation equation of elastic multilayered soils was then established with single drainage or double drainages under multilevel loading.Moreover,the formulas for calculating effective stress and settlement were derived from the Laplace numerical inversion transform.The three-dimensional composite analysis method of bridge pile group was improved,where the actual load conditions of pile foundation could be simulated,and the consolidation characteristics of soil layers beneath pile were also taken into account.Eventually,a corresponding program named LTPGS was developed to improve the calculation efficiency.The comparison between long-term settlement obtained from the proposed method and the in-situ measurements of pile foundation was illustrated,and a close agreement is obtained.The error between computed and measured results is less than 1 mm,and it gradually reduces with time.It is shown that the proposed method can effectively simulate the long-term settlement of pile foundation and program LTPGS can provide a reliable estimation.
基金Supported by the National Natural Science Foundation of China(10775105)
文摘Based on a newly revised inverse scattering transform for the derivative nonlinear SchrSdinger （DNLS＋） equation with nonvanishing boundary condition （NVBC）, the explicit breather- type and pure N-soliton solution has been derived by some algebra techniques. The two-breather solution and the pure double-soliton solution have been given as two typical examples in illustration of the general formula of the multi-soliton solution. The asymptotic behaviors of the N-soliton solution are discussed in detail.
基金Project supported by the National Natural Science Foundation of China (No.10172038)
文摘Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.
基金Supported by the Teaching Steering Committee Research Project of Higher-Learning Institutions of Ministry of Education(JZW-16-DD-15)
文摘A newly revised inverse scattering transform（IST） is used to solve the derivative nonlinear Schr？dinger（DNLS-＋） equation with non-vanishing boundary condition（NVBC） and normal group-velocity dispersion, and a mixed type of soliton solution is found, which is composed of both pure and breather-type solitons. The mixed-soliton solution can degenerate into breathers and pure solitons when taking the limit of some special parameters, proving the validity of the mixed-type solution.
基金Supported by the National Natural Science Foundation of China(10775105)
文摘A newly revised inverse scattering transform（IST） for the derivative nonlinear Schrdinger（DNLS＋） equation with non-vanishing boundary condition（NVBC） and normal group velocity dispersion is proposed by introducing a suitable affine parameter in Zakharov-Shabat integral kern.The explicit breather-type one-soliton solution,which can reproduce one pure soliton at the de-generate case and one bright soliton solution at the limit of van-ishing boundary,has been derived to verify the validity of the revised IST.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10474076 and 10375041
文摘One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10371070,10671121the Foundation of Shanghai Education Committee for Shanghai Prospective Excellent Young Teachers+1 种基金Shanghai Leading Academic Discipline Project under Grant No.J50101 the President Foundation of East China Institute of Technology under Grant No.DHXK0810
文摘N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources andthe hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scatteringtransform.
文摘In this paper,a time-frequency associated multiple signal classification(MUSIC)al-gorithm which is suitable for through-wall detection is proposed.The technology of detecting hu-man targets by through-wall radar can be used to monitor the status and the location information of human targets behind the wall.However,the detection is out of order when classical MUSIC al-gorithm is applied to estimate the direction of arrival.In order to solve the problem,a time-fre-quency associated MUSIC algorithm suitable for through-wall detection and based on S-band stepped frequency continuous wave(SFCW)radar is researched.By associating inverse fast Fouri-er transform(IFFT)algorithm with MUSIC algorithm,the power enhancement of the target sig-nal is completed according to the distance calculation results in the time domain.Then convert the signal to the frequency domain for direction of arrival(DOA)estimation.The simulations of two-dimensional human target detection in free space and the processing of measured data are com-pleted.By comparing the processing results of the two algorithms on the measured data,accuracy of DOA estimation of proposed algorithm is more than 75%,which is 50%higher than classical MUSIC algorithm.It is verified that the distance and angle of human target can be effectively de-tected via proposed algorithm.
基金supported in part by NSFC(11975145 and 11972291)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17 KJB 110020)。
文摘The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.
基金Supported by the National Natural Science Foundation of China under Project Nos.11331008 and 11171312the Collaborative Innovation Center for Aviation Economy Development of Henan Province
文摘The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. Then the Riemann–Hilbert problem corresponding to the reflection-less case is solved.As applications, multi-soliton solutions are obtained for the coupled Sasa–Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons.
基金Supported by the National Natural Science Foundation of China under Grant No.11071157Shanghai Leading Academic Discipline Project under Grant No.J50101
文摘N-lump solutions of the Kadomtsev-Petviashvili I equation in non-uniform media are derived through the inverse scattering transform. The obtained solutions describe lump waves with time-dependent amplitudes and velocities. Dynamics of l-lump wave and interactions of two lump wave are illustrated.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10534030 and 10375041
文摘Since the Jost solutions of the DNLS equation does not tend to the free Jost solutioins as ｜λ｜→∞, the usual inverse scattering transform （IST） must be revised. Beside the Kaup and Newell＇s approach, we propose a simple revision in constructing the equations of IST, where the usual Zakharov-Shabat kern is revised by multiplying λ^-2 or λ^-1. To justify the revision we show that the Jost solutions obtained do satisfy the pair of compatibility equations.
基金Supported by NBHM,Mumbai,under Department of Atomic Energy,Government of India vide Grant No.2/48(7)/2015/NBHM(R.P.)/R&D Ⅱ/11403
文摘In the present paper the Riesz fractional coupled Schr6dinger-Boussinesq （S-B） equations have been solved by the time-splitting Fourier spectral （TSFS） method. This proposed technique is utilized for discretizing the Schrodinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.
