sine-Gordon型方程的无穷序列新解  

New infinite sequence solutions to equations of sine-Gordon type

作　　者：套格图桑[1] 伊丽娜[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》2014年第21期5-13,共9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：通过下列步骤,获得了sine-Gordon型方程的新解.第一步、通过函数变换,把sine-Gordon方程与sinhGordon方程的求解问题转化为两种非线性常微分方程的求解问题.第二步、获得了两种非线性常微分方程与第一种椭圆方程的拟B?cklund变换.第三步、利用第一种椭圆方程的B?cklund变换与新解,构造了sine-Gordon型方程的无穷序列新解.The following steps are given to search for new solutions to equations of sine-Gordon type. Step one, according to function transformation, the solving of sine-Gordon equation and sinh-Gordon equation is changed into the solving of two kinds of nonlinear ordinary differential equations. Step two, two kinds of nonlinear ordinary differential equations and quasi-B℃ cklund transformation of the first kind of elliptic equation are obtained. Finally, new infinite sequence solutions to equations of sine-Gordon type are constructed by applying B℃ cklund transformation and new solutions of the first kind of elliptic equation.

关 键 词：函数变换 sine-Gordon型方程 第一种椭圆方程 无穷序列新解 

分 类 号：O175.29[理学—数学]