广义变系数KdV方程的Painlevé分析和自Bcklund变换  

Painlevé Analysis and Auto-Bcklund Transformations for the General Variable Coefficient KdV Equation

作　　者：许晓革[1] 魏光美[1] 

机构地区：[1]北京航空航天大学理学院

出　　处：《中国矿业大学学报》2008年第5期725-728,共4页Journal of China University of Mining & Technology

基　　金：北京市优秀人才资助项目(20061D0500700171)

摘　　要：利用符号计算对系数函数是x和t的函数的广义变系数KdV方程进行了Painlev啨分析,将方程解的广义Laurent展开式u(x,t)=p(x,t)∑∞j=0uj(t)j(x,t)代入方程,整理的各次幂的系数并令其为零,得到p的值以及关于uj的递推关系及共振点,由其相容条件恒成立知原方程具有Painlev啨性质.同时利用Painlev啨截断法给出了广义变系数KdV方程的一个自Bcklund变换,自Bcklund变换是联系同一个偏微分方程的解的变换,通过方程的一个解可以求出方程的另一个解,作为例子根据得到的自Bcklund变换给出了方程的两组精确解.With symbolic computation, a Painleve analysis for the KdV （gvc KdV） equation is carried out. The Laurent expansion general variable coefficient KdV（gve KdV）equation is carried out.The Laurent expansion equation u（x,t）=Ф^p（x,t）∑∞j=0uj（t）Ф^j（x,t） is substituted into the gvcKdV equation and recursive relations and resonant points are obtained. Since its conditions are consistent, the equation meets the conditions for a Painleve analysis. Using the Painleve truncation method, an auto-Backlund transformation is presented. The auto-Backlund transformation is a system of equations relating the solution of a given equation to another solution of the same equation. Under the auto-Backlund transformation, analytic solutions can be obtained, including solitonic profiles. To illustrate, two families of analytic solitonic solutions are presented via the auto-Backlund transformation.

关 键 词：广义变系数KdV方程 PAINLEVE分析 自B/icklund变换 符号计算 

分 类 号：O175.29[理学—数学] O411.2[理学—基础数学]