(2+1)维广义Calogero-Bogoyavlenskii-Schiff方程的无穷序列类孤子解  

New infinite sequence soliton-like solutions of (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

作　　者：套格图桑[1] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《物理学报》2013年第21期12-18,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11361040);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：为了构造高维非线性发展方程的无穷序列类孤子新解,研究了二阶常系数齐次线性常微分方程,获得了新结论.步骤一,给出一种函数变换把二阶常系数齐次线性常微分方程的求解问题转化为一元二次方程和Riccati方程的求解问题.在此基础上,利用Riccati方程解的非线性叠加公式,获得了二阶常系数齐次线性常微分方程的无穷序列新解.步骤二,利用以上得到的结论与符号计算系统Mathematica,构造了(2+1)维广义Calogero-Bogoyavlenskii-Schiff(GCBS)方程的无穷序列类孤子新解.This paper will study in detail homogeneous linear ordinary dll-terentml equation wire constant coemclents oI secona oraer ana draw new conclusion to construct new infinite sequence soliton-like solutions of high-dimensional nonlinear evolution equations. Step one： the solving of a homogeneous linear ordinary differential equation with constant coefficients of second order is changed into the solving of the quadratic equation with one unknown and the Riccati equation. Based on this, new infinite sequence solutions of ho- mogeneous linear ordinary differential equation with constant coefficients of second order are found by using nonlinear superposition formula for the solutions to Riccati equation. Step two： new infinite sequence soliton-like solutions to （2 ＋ 1）-dimensional gener- alized Calogero-Bogoyavlenskii-Schiff equation are constructed using the above conclusion and the symbolic computation system Mathematica.

关 键 词：常微分方程 非线性叠加公式 高维非线性发展方程 无穷序列类孤子新解 

分 类 号：O175.29[理学—数学]