This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries （KdV） equation and a coupled modified Korteweg-de Vries （mKdV）...This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries （KdV） equation and a coupled modified Korteweg-de Vries （mKdV） equation. This method provides a sequence Of functions which converges to the exact solution of the problem and is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.展开更多
The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈...The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈 2, and the probability density function ω（t） of a particle＇s waiting time t follows a power law form for large t： ω（t） ～t^-（1＋α）, 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.展开更多
We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,...We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.展开更多
A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed, which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling. This model allo...A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed, which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling. This model allows ballistic diffusion and classical localization simultaneously, in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken. The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium, however, when the system starts from nonthermal conditions, it does not approach the equilibration even though a nonlinear potential is used to bound the particle, this can be confirmed by the zerotb law of thermodynamics. In the dynamics of Brownian localization, due to the memory damping function inducing a constant term, our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum. The coupled oscillator chain with a fixed end boundary acts as a heat bath, which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration, we investigate this problem from the viewpoint of nonergodicity.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10771019 and 10826107)
文摘This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries （KdV） equation and a coupled modified Korteweg-de Vries （mKdV） equation. This method provides a sequence Of functions which converges to the exact solution of the problem and is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11605003 and 11547231
文摘The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈 2, and the probability density function ω（t） of a particle＇s waiting time t follows a power law form for large t： ω（t） ～t^-（1＋α）, 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.
基金Project supported by the Global Change Research Program of China(Grant No.2015CB953904)the National Natural Science Foundation of China(Grant Nos.11275072 and 11435005)+2 种基金the Doctoral Program of Higher Education of China(Grant No.20120076110024)the Network Information Physics Calculation of Basic Research Innovation Research Group of China(Grant No.61321064)Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things,China(Grant No.ZF1213)
文摘We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.
基金supported by the National Natural Science Foundation of China (Grant No. 11175021)
文摘A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed, which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling. This model allows ballistic diffusion and classical localization simultaneously, in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken. The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium, however, when the system starts from nonthermal conditions, it does not approach the equilibration even though a nonlinear potential is used to bound the particle, this can be confirmed by the zerotb law of thermodynamics. In the dynamics of Brownian localization, due to the memory damping function inducing a constant term, our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum. The coupled oscillator chain with a fixed end boundary acts as a heat bath, which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration, we investigate this problem from the viewpoint of nonergodicity.
