sine-Gordon型方程的无穷序列新精确解  

New infinite sequences exact solutions to sine-Gordon-type equations

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》2011年第7期12-24,共13页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10461006);内蒙古自治区高等学校科学研究基金(批准号:NJZZ07031);内蒙古自治区自然科学基金(批准号:2010MS0111)资助的课题~~

摘　　要：为了获得sine-Gordon型方程的无穷序列精确解,给出三角函数型辅助方程和双曲函数型辅助方程及其Bcklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,构造了sine-Gordon方程、mKdV-sine-Gordon方程、(n+1)维双sine-Gordon方程和sinh-Gordon方程的无穷序列新精确解.其中包括无穷序列三角函数解、无穷序列双曲函数解、无穷序列Jacobi椭圆函数解和无穷序列复合型解.In order to obtain infinite sequence exact solutions to the sine-Gordon-type equations, the auxiliary equations of triangular function type and hyperbolic function type, Backlund transformation and nonlinear superposition formula of the solutions are presented. And the method is used to construct new infinite sequence exact solutions to the sine-Gordon equation, mKdV-sine-Gordon equation, （ n ＋ 1 ） - dimensional double sine-Gordon equation and the sinh-Gordon equation with the help of symbolic computation system Mathematica, which include infinite sequence triangular function solutions, the infinite sequence hyperbolic function solutions, infinite sequence Jacobi elliptic function solutions and infinite sequence computation solutions.

关 键 词：sine-Gordon型方程 解的非线性叠加公式 辅助方程 无穷序列精确解 

分 类 号：O175.29[理学—数学]