构造非线性发展方程无穷序列类孤子精确解的一种方法  

A method of constructing infinite sequence soliton-like solutions of nonlinear evolution equations

作　　者：套格图桑[1,2] 白玉梅[1] 

机构地区：[1]内蒙古民族大学数学学院,通辽028043 [2]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《物理学报》2012年第13期18-25,共8页Acta Physica Sinica

基　　金：国家自然科学基金资助项目(批准号:10862003);内蒙古自治区高等学校科学研究基金(批准号:NJZY12031);内蒙古自治区自然科学基金(批准号:2010MS0111)资助的课题~~

摘　　要：辅助方程法已构造了非线性发展方程的有限多个新精确解.本文为了构造非线性发展方程的无穷序列类孤子精确解,分析总结了辅助方程法的构造性和机械化性特点.在此基础上,给出了一种辅助方程的新解与Riccati方程之间的拟Bcklund变换.选择了非线性发展方程的两种形式解,借助符号计算系统Mathematica,用改进的(2+1)维色散水波系统为应用实例,构造了该方程的无穷序列类孤子新精确解.这些解包括无穷序列光滑类孤子解,紧孤立子解和尖峰类孤立子解.The auxiliary equation method is used to construct the finite new exact solutions of nonlinear evolution equations. To search for infinite sequence soliton-like exact solutions of nonlinear evolution equations, characteristics of constructivity and mechanization of auxiliary equation method are analyzed and summarized. Therefore, the quasi-B^icklund transformation between new solutions of a kind of auxiliary equation with Riccati equation is presented, then （2＋l）-dimensional modified dispersive water-wave system is taken as an applicable example to find infinite sequence soliton-like new exact solutions by choosing two kinds of formal solutions of nonlinear evolution equations with the help of symbolic computation system Mathematica, where included are the infinite sequence smooth soliton-like solutions, compact soliton solutions and peak stilton-like solutions.

关 键 词：辅助方程 非线性发展方程 Bcklund变换 类孤子新精确解 

分 类 号：O175.29[理学—数学]