By employing the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method is presented for the unsteady Schrodinger equation. In the IEFG method, the two-dimensional (2D...By employing the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method is presented for the unsteady Schrodinger equation. In the IEFG method, the two-dimensional (2D) trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square (MLS) approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.展开更多
The nonlinear Schr6dinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the dis...The nonlinear Schr6dinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.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
In this paper, some two-grid finite element schemes are constructed for solving the nonlinear SchrSdinger equation. With these schemes, the solution of the original problem is reduced to the solution of the same probl...In this paper, some two-grid finite element schemes are constructed for solving the nonlinear SchrSdinger equation. With these schemes, the solution of the original problem is reduced to the solution of the same problem on a much coarser grid together with the solutions of two linear problems on a fine grid. We have shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy.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
The South China Sea (SCS) is a hot spot for oceanic internal solitary waves due to many factors, such as the complexity of the terrain environment. The internal solitary waves in the northern SCS mainly originate in...The South China Sea (SCS) is a hot spot for oceanic internal solitary waves due to many factors, such as the complexity of the terrain environment. The internal solitary waves in the northern SCS mainly originate in the Luzon Strait. The generation mechanism of the internal solitary waves in the Luzon Strait is discussed using a modulation instability. The energy gain of the modulation instability is derived based on the fully nonlinear Schr6dinger equation. The peak value of the gain is calculated under different conditions of stratification, wavelength and the initial amplitude of an internal tidal wave. The characteristics of the modulation instability in the Luzon Strait are investigated. The conditions that make the internal tidal wave evolve into an internal solitary wave in the Luzon strait are also obtained. The results show that the internal tide waves can generate the modulation instability in the Luzon Strait and that the maximum gain occur at the eastern sill of the Luzon Strait, where the internal tide waves start to break up into internal solitary trains. The magnitude and the scope of the peak gain are relevant to the stratification and the initial conditions of the internal tide waves. The numerical simulation results are consistent with the in-situ data.展开更多
Nonlinear mechanics for a super-thin elastic rod with the biological background of DNA super-coiling macromolecules is an interdisciplinary research area of classical mechanics and molecular biology. It is also a subj...Nonlinear mechanics for a super-thin elastic rod with the biological background of DNA super-coiling macromolecules is an interdisciplinary research area of classical mechanics and molecular biology. It is also a subject of dynamics and elasticity because elastic bodies are analyzed via the theory of dynamics. It is in frontiers of general mechanics (dynamics and control). This dissertation is devoted to model a constrained super-thin elastic rod and analyze its stability in equilibrium. The existing research results are summarized. Analytical mechanics is systematically applied to model the elastic rod. The Schroedinger equation for complex curvatures or complex bending moments is, respectively, extended from the case of circular crosssections to that of non-circular ones. The equilibrium of a rod constrained on a surface is investigated.展开更多
We study the spherical quantum pseudodots in the Schr6dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite en...We study the spherical quantum pseudodots in the Schr6dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave functions are calculated. Furthermore, the behavior of the essential thermodynamic quantities such as, the free energy, the mean energy, the entropy, the specific heat, the magnetization, the magnetic susceptibility, and the persistent currents are also studied by using the characteristic function. Our analytical results are found to be in good agreement with the other works. The numerical results on the energy levels as well as the thermodynamic quantities have also been given.展开更多
We need to solve a suitable exponential form of the position-dependent mass (PDM) Schr6dinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the ext...We need to solve a suitable exponential form of the position-dependent mass (PDM) Schr6dinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the external magnetic and Aharonov-Bohm (AB) flux fields. The bound state energies and their corresponding wave functions are calculated for the spatially-dependent mass distribution function of interest in physics. A few plots of some numerical results with respect to the energy are shown.展开更多
With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order trunca...With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized.They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving,but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrdinger equations.In particular,they are much better than the optimal third-order non-gradient symplectic method.They also have an advantage over the fourth-order non-gradient symplectic integrator.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11171208)the Natural Science Foundation of Zhejiang Province,China(Grant No.LY15A020007)+1 种基金the Natural Science Foundation of Ningbo City(Grant No.2014A610028)the K.C.Wong Magna Fund in Ningbo University,China
文摘By employing the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method is presented for the unsteady Schrodinger equation. In the IEFG method, the two-dimensional (2D) trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square (MLS) approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.
基金Project supported by the National Natural Science Foundation of China (Grant No.11101191)
文摘The nonlinear Schr6dinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.
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Acknowledgments. This work is partially supported by National Science Foundation of China (10971059), Young Scientists Foundation of the National Science Foundation of China (11101136), Hunan Provincial Natural Science Foundation of China (14JJ2114), Science and Technology Foundation of Hunan Province (2013FJ4229).
文摘In this paper, some two-grid finite element schemes are constructed for solving the nonlinear SchrSdinger equation. With these schemes, the solution of the original problem is reduced to the solution of the same problem on a much coarser grid together with the solutions of two linear problems on a fine grid. We have shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy.
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The National Natural Science Foundation of China under contract No.61171161
文摘The South China Sea (SCS) is a hot spot for oceanic internal solitary waves due to many factors, such as the complexity of the terrain environment. The internal solitary waves in the northern SCS mainly originate in the Luzon Strait. The generation mechanism of the internal solitary waves in the Luzon Strait is discussed using a modulation instability. The energy gain of the modulation instability is derived based on the fully nonlinear Schr6dinger equation. The peak value of the gain is calculated under different conditions of stratification, wavelength and the initial amplitude of an internal tidal wave. The characteristics of the modulation instability in the Luzon Strait are investigated. The conditions that make the internal tidal wave evolve into an internal solitary wave in the Luzon strait are also obtained. The results show that the internal tide waves can generate the modulation instability in the Luzon Strait and that the maximum gain occur at the eastern sill of the Luzon Strait, where the internal tide waves start to break up into internal solitary trains. The magnitude and the scope of the peak gain are relevant to the stratification and the initial conditions of the internal tide waves. The numerical simulation results are consistent with the in-situ data.
文摘Nonlinear mechanics for a super-thin elastic rod with the biological background of DNA super-coiling macromolecules is an interdisciplinary research area of classical mechanics and molecular biology. It is also a subject of dynamics and elasticity because elastic bodies are analyzed via the theory of dynamics. It is in frontiers of general mechanics (dynamics and control). This dissertation is devoted to model a constrained super-thin elastic rod and analyze its stability in equilibrium. The existing research results are summarized. Analytical mechanics is systematically applied to model the elastic rod. The Schroedinger equation for complex curvatures or complex bending moments is, respectively, extended from the case of circular crosssections to that of non-circular ones. The equilibrium of a rod constrained on a surface is investigated.
文摘We study the spherical quantum pseudodots in the Schr6dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave functions are calculated. Furthermore, the behavior of the essential thermodynamic quantities such as, the free energy, the mean energy, the entropy, the specific heat, the magnetization, the magnetic susceptibility, and the persistent currents are also studied by using the characteristic function. Our analytical results are found to be in good agreement with the other works. The numerical results on the energy levels as well as the thermodynamic quantities have also been given.
文摘We need to solve a suitable exponential form of the position-dependent mass (PDM) Schr6dinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the external magnetic and Aharonov-Bohm (AB) flux fields. The bound state energies and their corresponding wave functions are calculated for the spatially-dependent mass distribution function of interest in physics. A few plots of some numerical results with respect to the energy are shown.
基金supported by the NationalNatural Science Foundation of China (Grant No.10873007)supported by the Science Foundation of Jiangxi Education Bureau (Grant No.GJJ09072)the Program for Innovative Research Team of Nanchang University
文摘With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized.They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving,but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrdinger equations.In particular,they are much better than the optimal third-order non-gradient symplectic method.They also have an advantage over the fourth-order non-gradient symplectic integrator.