截断展开方法和广义变系数KdV方程新的精确类孤子解  

TRUNCATED EXPANSION METHOD AND NEW EXACT SOLITON-LIKE SOLUTION OF THE GENERAL VARIABLE COEFFICIENT KdV EQUATION

作　　者：张解放[1] 陈芳跃[2] 

机构地区：[1]浙江师范大学非线性物理研究室,金华321004 [2]浙江师范大学数学研究所,金华321004

出　　处：《物理学报》2001年第9期1648-1650,共3页Acta Physica Sinica

摘　　要：利用特殊的截断展开方法求出了广义变系数KdV方程新的类孤子解 .这种方法的基本思想是假定形式解具有截断展开形式 ,以致可把广义变系数KdV方程转化为一组待定函数的代数方程组 ,进而给出待定函数容易积分的常微分方程 .利用例子证明了这种方法是十分有效的 .By using of the special truncated expansion, the soliton-like solution of the generalized KdV equation with variable coefficients is obtained. In this method, the form solution is assumed as the truncated expansion form which is based on the idea that the generalized KdV equation with variable coefficients is reduced to a set of algebraic equations of undetermined functions, so that we can obtain a set of ordinary differential equations of undetermined functions which are easily integrated. An example is given to illustrated that this method is very effective in solving soliton-like solution of a large class of variable coefficient nonlinear evolution equations.

关 键 词：截断展开法 广义变系数 KDV方程 孤子解 非线性理论 量子力学 

分 类 号：O175[理学—数学]