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
Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generali...Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.展开更多
We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear...We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear Schr¨odinger equation.Beyond the fundamental nondegenerate one-soliton solution,we have identified and characterized nondegenerate breather bound state solitons,with particular emphasis on their evolution dynamics.展开更多
This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Ca...This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated equations.In this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions.These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem.Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction.These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.展开更多
We introduce a novel neural network structure called strongly constrained theory-guided neural network(SCTgNN),to investigate the behaviour of the localized solutions of the generalized nonlinear Schr?dinger(NLS)equat...We introduce a novel neural network structure called strongly constrained theory-guided neural network(SCTgNN),to investigate the behaviour of the localized solutions of the generalized nonlinear Schr?dinger(NLS)equation.This equation comprises four physically significant nonlinear evolution equations,namely,the NLS,Hirota,Lakshmanan-Porsezian-Daniel and fifth-order NLS equations.The generalized NLS equation demonstrates nonlinear effects up to quintic order,indicating rich and complex dynamics in various fields of physics.By combining concepts from the physics-informed neural network and theory-guided neural network(TgNN)models,the SCTgNN aims to enhance our understanding of complex phenomena,particularly within nonlinear systems that defy conventional patterns.To begin,we employ the TgNN method to predict the behaviour of localized waves,including solitons,rogue waves and breathers,within the generalized NLS equation.We then use the SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both the SCTgNN and TgNN in predicting these three localized solutions.Our findings reveal that both models excel in understanding complex behaviour and provide predictions across a wide variety of situations.展开更多
For systems modeled by the resonant nonlinear Schrödinger equation(RNLSE)with generalized cubic-quintic nonlinearity,we derive the bright soliton solution of the equation in(1+1)dimensions,using the modified F-ex...For systems modeled by the resonant nonlinear Schrödinger equation(RNLSE)with generalized cubic-quintic nonlinearity,we derive the bright soliton solution of the equation in(1+1)dimensions,using the modified F-expansion method along with the novel ansatz of F-base function.Furthermore,we extend the analytical study of soliton dynamics to higher(2+1)and(3+1)dimensions by using the self-similar method,and demonstrate the soliton behavior via graphical illustration.Moreover,we investigate the effect of the resonance term on bright soliton solution in(1+1)dimensions.Additionally,we consider the nonlinear equation models with perturbation terms and derive the bright soliton solutions for the one-dimensional(1D)to three-dimensional(3D)cases.The theoretical results derived can be used to guide the experimental studies and observations of bright solitons in systems described by RNLSE model.展开更多
In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L<sup>2</sup>-supercriti...In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L<sup>2</sup>-supercritical case, we obtain the existence and stability of standing waves. Our results are complements to the results of Carles and Il’yasov’s artical, where orbital stability of standing waves have been studied for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.展开更多
This paper studies the existence of stable standing waves for the nonlinear Schrödinger equation with Hartree-type nonlinearity i∂tψ+Δψ+| ψ |pψ+(| x |−γ∗| ψ |2)ψ=0, (t,x)∈[ 0,T )×ℝN.Where ψ=ψ(t,...This paper studies the existence of stable standing waves for the nonlinear Schrödinger equation with Hartree-type nonlinearity i∂tψ+Δψ+| ψ |pψ+(| x |−γ∗| ψ |2)ψ=0, (t,x)∈[ 0,T )×ℝN.Where ψ=ψ(t,x)is a complex valued function of (t,x)∈ℝ+×ℝN. The parameters N≥3, 0p4Nand 0γmin{ 4,N }. By using the variational methods and concentration compactness principle, we prove the orbital stability of standing waves.展开更多
We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localiz...We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localized wave solution,the N-fold generalized Darboux transformation is given.Under the condition that the characteristic equation admits a double-root,we present the expression of the first-order interactional solution.Then we graphically analyze the dynamics of the breather and rogue wave.Due to the simultaneous existence of nonlinear and self-steepening terms in the equation,different profiles in two components for the breathers are presented.展开更多
We construct various novel exact solutions of two coupled dynamical nonlinear Schrōdinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrōdinger equations with time-and space-...We construct various novel exact solutions of two coupled dynamical nonlinear Schrōdinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrōdinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrrdinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.展开更多
In this work, we present the direct discontinuous Galerkin （DDG） method for the one-dimensional coupled nonlinear Schr5dinger （CNLS） equation. We prove that the new discontinuous Galerkin method preserves the disc...In this work, we present the direct discontinuous Galerkin （DDG） method for the one-dimensional coupled nonlinear Schr5dinger （CNLS） equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.展开更多
We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota b...We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.展开更多
In this paper, the improved Adomian decomposition method (ADM) is applied to the nonlinear Schrödinger’s equation (NLSE), one of the most important partial differential equations in quantum mechanics that gov...In this paper, the improved Adomian decomposition method (ADM) is applied to the nonlinear Schrödinger’s equation (NLSE), one of the most important partial differential equations in quantum mechanics that governs the propagation of solitons through optical fibers. The performance and the accuracy of our improved method are supported by investigating several numerical examples that include initial conditions. The obtained results are compared with the exact solutions. It is shown that the method does not need linearization, weak or perturbation theory to obtain the solutions.展开更多
In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule o...In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.展开更多
This paper considers the one-dimensional dissipative cubic nonlinear SchrSdinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-lev...This paper considers the one-dimensional dissipative cubic nonlinear SchrSdinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.展开更多
The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type ...The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.展开更多
We derive an N-fold Darboux transformation for the nonlinear Schrdinger equation coupled to a multiple selfinduced transparency system, which is applicable to optical fiber communications in the erbium-doped medium.Th...We derive an N-fold Darboux transformation for the nonlinear Schrdinger equation coupled to a multiple selfinduced transparency system, which is applicable to optical fiber communications in the erbium-doped medium.The N-soliton, N-breather and N th-order rogue wave solutions in the compact determinant representations are derived using the Darboux transformation and limit technique. Dynamics of such solutions from the first-to second-order ones are shown.展开更多
The stability of a set of spatially constant plane wave solutions to a pair of damped coupled nonlinear Schrödinger evolution equations is considered. The equations could model physical phenomena arising in fluid...The stability of a set of spatially constant plane wave solutions to a pair of damped coupled nonlinear Schrödinger evolution equations is considered. The equations could model physical phenomena arising in fluid dynamics, fibre optics or electron plasmas. The main result is that any small perturbation to the solution remains small for all time. Here small is interpreted as being both in the supremum sense and the square integrable sense.展开更多
By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrdinger equation are derived. In the limit c...By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrdinger equation are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.展开更多
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 supported by the National Natural Science Foundation of China(Grant No.12271096)the Natural Science Foundation of Fujian Province(Grant No.2021J01302)。
文摘Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.
基金supported by the National Natural Science Foundation of China(Grant Nos.12261131495 and 12475008)the Scientific Research and Developed Fund of Zhejiang A&F University(Grant No.2021FR0009)。
文摘We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear Schr¨odinger equation.Beyond the fundamental nondegenerate one-soliton solution,we have identified and characterized nondegenerate breather bound state solitons,with particular emphasis on their evolution dynamics.
基金supported by the National Natural Science Foundation of China(No.12271334).
文摘This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated equations.In this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions.These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem.Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction.These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.
基金the Science and Engineering Research Board,Government of India for Grant No.CRG/2021/002428DST-SERB,Government of India for providing the National Post-Doctoral Fellowship under Grant No.PDF/2023/000619+2 种基金the Department of Science and Technology (DST),India,for the financial support under the Women Scientist Scheme-Asupported by the Science and Engineering Research Board,Government of India,under Grant No.CRG/2021/002428MoE-RUSA 2.0 Physical Sciences,Government of India,for sponsoring this research work。
文摘We introduce a novel neural network structure called strongly constrained theory-guided neural network(SCTgNN),to investigate the behaviour of the localized solutions of the generalized nonlinear Schr?dinger(NLS)equation.This equation comprises four physically significant nonlinear evolution equations,namely,the NLS,Hirota,Lakshmanan-Porsezian-Daniel and fifth-order NLS equations.The generalized NLS equation demonstrates nonlinear effects up to quintic order,indicating rich and complex dynamics in various fields of physics.By combining concepts from the physics-informed neural network and theory-guided neural network(TgNN)models,the SCTgNN aims to enhance our understanding of complex phenomena,particularly within nonlinear systems that defy conventional patterns.To begin,we employ the TgNN method to predict the behaviour of localized waves,including solitons,rogue waves and breathers,within the generalized NLS equation.We then use the SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both the SCTgNN and TgNN in predicting these three localized solutions.Our findings reveal that both models excel in understanding complex behaviour and provide predictions across a wide variety of situations.
基金Project supported by the National Natural Science Foundation of China(Grant No.11547024)。
文摘For systems modeled by the resonant nonlinear Schrödinger equation(RNLSE)with generalized cubic-quintic nonlinearity,we derive the bright soliton solution of the equation in(1+1)dimensions,using the modified F-expansion method along with the novel ansatz of F-base function.Furthermore,we extend the analytical study of soliton dynamics to higher(2+1)and(3+1)dimensions by using the self-similar method,and demonstrate the soliton behavior via graphical illustration.Moreover,we investigate the effect of the resonance term on bright soliton solution in(1+1)dimensions.Additionally,we consider the nonlinear equation models with perturbation terms and derive the bright soliton solutions for the one-dimensional(1D)to three-dimensional(3D)cases.The theoretical results derived can be used to guide the experimental studies and observations of bright solitons in systems described by RNLSE model.
文摘In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L<sup>2</sup>-supercritical case, we obtain the existence and stability of standing waves. Our results are complements to the results of Carles and Il’yasov’s artical, where orbital stability of standing waves have been studied for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.
文摘This paper studies the existence of stable standing waves for the nonlinear Schrödinger equation with Hartree-type nonlinearity i∂tψ+Δψ+| ψ |pψ+(| x |−γ∗| ψ |2)ψ=0, (t,x)∈[ 0,T )×ℝN.Where ψ=ψ(t,x)is a complex valued function of (t,x)∈ℝ+×ℝN. The parameters N≥3, 0p4Nand 0γmin{ 4,N }. By using the variational methods and concentration compactness principle, we prove the orbital stability of standing waves.
基金the National Natural Science Foundation of China(Grant Nos.11871232 and 12201578)Natural Science Foundation of Henan Province,China(Grant Nos.222300420377 and 212300410417)。
文摘We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localized wave solution,the N-fold generalized Darboux transformation is given.Under the condition that the characteristic equation admits a double-root,we present the expression of the first-order interactional solution.Then we graphically analyze the dynamics of the breather and rogue wave.Due to the simultaneous existence of nonlinear and self-steepening terms in the equation,different profiles in two components for the breathers are presented.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11275072,11075055,and 11271211)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120076110024)+3 种基金the Innovative Research Team Program of the National Natural Science Foundation of China(Grant No.61021004)the Shanghai Leading Academic Discipline Project,China(Grant No.B412)the National High Technology Research and Development Program of China(Grant No.2011AA010101)the Shanghai Knowledge Service Platform for Trustworthy Internet of Things,China(Grant No.ZF1213)
文摘We construct various novel exact solutions of two coupled dynamical nonlinear Schrōdinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrōdinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrrdinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.
基金Project supported by the National Natural Science Foundation of China （Grant No 11171038）.
文摘In this work, we present the direct discontinuous Galerkin （DDG） method for the one-dimensional coupled nonlinear Schr5dinger （CNLS） equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.
基金supported by the National Natural Science Foundation of China (Grant Nos.11975204 and 12075208)the Project of Zhoushan City Science and Technology Bureau (Grant No.2021C21015)the Training Program for Leading Talents in Universities of Zhejiang Province。
文摘We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.
文摘In this paper, the improved Adomian decomposition method (ADM) is applied to the nonlinear Schrödinger’s equation (NLSE), one of the most important partial differential equations in quantum mechanics that governs the propagation of solitons through optical fibers. The performance and the accuracy of our improved method are supported by investigating several numerical examples that include initial conditions. The obtained results are compared with the exact solutions. It is shown that the method does not need linearization, weak or perturbation theory to obtain the solutions.
基金Supported by the National Natural Science Foundation of China under Grant No.11271210the K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.
文摘This paper considers the one-dimensional dissipative cubic nonlinear SchrSdinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.
文摘The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11705290 and 11305060the China Postdoctoral Science Foundation under Grant No 2016M602252
文摘We derive an N-fold Darboux transformation for the nonlinear Schrdinger equation coupled to a multiple selfinduced transparency system, which is applicable to optical fiber communications in the erbium-doped medium.The N-soliton, N-breather and N th-order rogue wave solutions in the compact determinant representations are derived using the Darboux transformation and limit technique. Dynamics of such solutions from the first-to second-order ones are shown.
文摘The stability of a set of spatially constant plane wave solutions to a pair of damped coupled nonlinear Schrödinger evolution equations is considered. The equations could model physical phenomena arising in fluid dynamics, fibre optics or electron plasmas. The main result is that any small perturbation to the solution remains small for all time. Here small is interpreted as being both in the supremum sense and the square integrable sense.
文摘By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrdinger equation are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.
