In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the sol...In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.展开更多
This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis techniq...This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.展开更多
In this article, two split-step finite difference methods for Schrodinger-KdV equations are formulated and investigated. The main features of our methods are based on:(i) The applications of split-step technique for S...In this article, two split-step finite difference methods for Schrodinger-KdV equations are formulated and investigated. The main features of our methods are based on:(i) The applications of split-step technique for Schrodingerlike equation in time.(ii) The utilizations of high-order finite difference method for KdV-like equation in spatial discretization.(iii) Our methods are of spectral-like accuracy in space and can be realized by fast Fourier transform efficiently. Numerical experiments are conducted to illustrate the efficiency and accuracy of our numerical methods.展开更多
The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In part...The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.展开更多
In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigatio...In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigation but also monitor the optical power and dispersion profile over multi-span links.The link status information can be extracted by the characteristics of the learned optical fiber parameters without any other measuring instruments.The efficiency and feasibility of this method have been investigated in different fiber link conditions,including various launch power,transmission distance,and the location and the amount of the abnormal losses.A good monitoring performance can be obtained while the launch optical power is 2 dBm which does not affect the normal operation of the optical communication system and the step size of DBP is 20 km which can provide a better distance resolution.This scheme successfully detects the location of single or multiple optical attenuators in long-distance multi-span fiber links,including different abnormal losses of 2 dB,4 dB,and 6 dB in 360 km and serval combinations of abnormal losses of(1 dB,5 dB),(3 dB,3 dB),(5 dB,1 dB)in 360 km and 760 km.Meanwhile,the transfer relationship of the estimated coefficient values with different step sizes is further investigated to reduce the complexity of the fiber nonlinear damage compensation.These results provide an attractive approach for precisely sensing the optical fiber link status information and making correct strategies timely to ensure optical communication system operations.展开更多
Based on the equation satisfied by optical pulse that is a slowly varying function, the higher-order nonlinear Schr o¨dinger equation(NLSE) including Raman gain and self-steepening effect is deduced in detail, an...Based on the equation satisfied by optical pulse that is a slowly varying function, the higher-order nonlinear Schr o¨dinger equation(NLSE) including Raman gain and self-steepening effect is deduced in detail, and a new Raman gain function is defined. By using the split-step Fourier method, the influence of the combined effect between Raman gain and self-steepening on the propagation characteristic of dark solitons is simulated in the isotropic fiber. The results show that gray solitons can be symmetrically formed by high order dark soliton, however self-steepening effect will inhibit the formation mechanism through the phenomenon that gray solitons are produced only in the trailing edge of the central black soliton. Meanwhile, the Raman gain changes the propagation characteristic of optical soliton and inhibits the self-steepening effect, resulting in the broadening of pulse width and the decreasing of pulse offset.展开更多
文摘In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214)the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011)+1 种基金supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716)supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347).
文摘This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.
基金Supported by the National Natural Science Foundation of China under Grant No.11571181
文摘In this article, two split-step finite difference methods for Schrodinger-KdV equations are formulated and investigated. The main features of our methods are based on:(i) The applications of split-step technique for Schrodingerlike equation in time.(ii) The utilizations of high-order finite difference method for KdV-like equation in spatial discretization.(iii) Our methods are of spectral-like accuracy in space and can be realized by fast Fourier transform efficiently. Numerical experiments are conducted to illustrate the efficiency and accuracy of our numerical methods.
基金supported by the State Scholarship Fund of the China Scholarship Council (Grant 2009629129)
文摘The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.
基金supported by the National Key Research and Development Program of China (2019YFB1803905)the National Natural Science Foundation of China (No.62171022)+2 种基金Beijing Natural Science Foundation (4222009)Guangdong Basic and Applied Basic Research Foundation (2021B1515120057)the Scientific and Technological Innovation Foundation of Shunde Graduate School,USTB (No.BK19AF005)。
文摘In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigation but also monitor the optical power and dispersion profile over multi-span links.The link status information can be extracted by the characteristics of the learned optical fiber parameters without any other measuring instruments.The efficiency and feasibility of this method have been investigated in different fiber link conditions,including various launch power,transmission distance,and the location and the amount of the abnormal losses.A good monitoring performance can be obtained while the launch optical power is 2 dBm which does not affect the normal operation of the optical communication system and the step size of DBP is 20 km which can provide a better distance resolution.This scheme successfully detects the location of single or multiple optical attenuators in long-distance multi-span fiber links,including different abnormal losses of 2 dB,4 dB,and 6 dB in 360 km and serval combinations of abnormal losses of(1 dB,5 dB),(3 dB,3 dB),(5 dB,1 dB)in 360 km and 760 km.Meanwhile,the transfer relationship of the estimated coefficient values with different step sizes is further investigated to reduce the complexity of the fiber nonlinear damage compensation.These results provide an attractive approach for precisely sensing the optical fiber link status information and making correct strategies timely to ensure optical communication system operations.
基金The Open Issues of Jiangsu Key Lab of Solar Cell Materials and Technology(201207)the Open Issues of State Key Laboratory of Satellite Ocean Environment Dynamics of China(No.SOED1201)
基金supported by the National Natural Science Foundation of China(Grant No.61167004)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2014MS0104)
文摘Based on the equation satisfied by optical pulse that is a slowly varying function, the higher-order nonlinear Schr o¨dinger equation(NLSE) including Raman gain and self-steepening effect is deduced in detail, and a new Raman gain function is defined. By using the split-step Fourier method, the influence of the combined effect between Raman gain and self-steepening on the propagation characteristic of dark solitons is simulated in the isotropic fiber. The results show that gray solitons can be symmetrically formed by high order dark soliton, however self-steepening effect will inhibit the formation mechanism through the phenomenon that gray solitons are produced only in the trailing edge of the central black soliton. Meanwhile, the Raman gain changes the propagation characteristic of optical soliton and inhibits the self-steepening effect, resulting in the broadening of pulse width and the decreasing of pulse offset.
