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
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 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
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
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 have investigated the intensity squeezing of superposition of two photon-added coherent states and proposed a new method for preparation of photon-added coherent states and their superposition states.This method is...We have investigated the intensity squeezing of superposition of two photon-added coherent states and proposed a new method for preparation of photon-added coherent states and their superposition states.This method is based on interaction of the trapped ion with the traveling wave light fields with different frequencies.展开更多
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(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.
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.
基金Supported by the Natural Science Foundation of Anhui Province under Grant No. 090412060
文摘We have investigated the intensity squeezing of superposition of two photon-added coherent states and proposed a new method for preparation of photon-added coherent states and their superposition states.This method is based on interaction of the trapped ion with the traveling wave light fields with different frequencies.
