(1+1)维耦合Ito系统的单值和多值局域激发模式

在(1 1)维非线性动力学系统,人们发现不同的局域激发模式分别存在于不同的非线性系统.可是最近的若干研究表明,在高维非线性动力学系统中,如果选取适当的边值条件或初始条件时,人们可以同时找到若干不同的局域激发模式,如:紧致子、峰孤子、呼吸子和折叠子等.本文的主要目的是寻找(1 1)维非线性耦合Ito系统中的不同的局域激发模式.首先,基于一个特殊的Painlev-éBacklund变换和线性变量分离方法,求得了该系统具有若干任意函数的变量分离严格解.然后,根据得到的变量分离严格解,通过选择严格解中的任意函数,引入恰当的单值分段连续函数和多值局域函数,成功找到了耦合Ito系统若干有实际物理意义的单值和多值局域激发模式,如:峰孤子,紧致子和多圈孤子等.

Localized excitations with single and multiple valued evolutional properties for the coupled (1+1)-dimensional Ito system

In (1+1)-dimensional nonlinear dynamical systems, it is believed that different kinds of localized excitations exist in different types of nonlinear models respectively. However, in recent study on higher-dimensions, some important localized excitations like compactons, peakons, breathers and foldons etc. are simultaneously derived from a (2+1)-dimensional nonlinear model if choosing appropriate initial or boundary conditions. The main purpose of the present paper is searching for different types of solitary wave in a (1+1)-dimensional Ito system. variable separation approach, the coupled Ito system is successfully solved and a general variable separation excitation with two arbitrary functions for the coupled Ito system is obtained. Then based on the derived variable separation excitation and by selecting the arbitrary functions in the exact solution appropriately, such as certain piecewise smooth functions and multi-valued localized functions, many significant types of localized excitations such as compactons, peakons and looped solitary waves are simultaneously obtained from the coupled (1+1)-dimensional Ito system.