广义变系数KdV,mKdV方程的精确类孤子解  

Exact solitude-like solutions to generalized KdV and mKdV equations with variable coefficients

作　　者：张玉峰[1] 孔令臣[1] 杨耕文[2] 

机构地区：[1]山东科技大学 [2]洛阳大学,河南洛阳471000

出　　处：《甘肃工业大学学报》2002年第3期115-117,共3页Journal of Gansu University of Technology

基　　金：国家自然科学基金 (10 0 72 0 13 ) ;国家重点基础发展规划项目 (G19980 3 60 0 )

摘　　要：利用截断展开法和延拓齐次平衡法同时求出了广义变系数KdV方程和广义变系数mKdV方程的精确钟状类孤子解 .其基本思想是 :设方程的解形式为u(x ,t) =∑nm=0υm(t)Fm,　F =eα( ξ+ξ0 )1+eα( ξ+ξ0 )代入给定方程确定出n ,并令F的各次幂项的系数为零 ,得到超定可积分方程组 ,由此求出给定方程的精确类孤子解 .Exact bell shaped solitary solutions for the generalized KdV and mKdV equations with variable coefficients are obtained by the use of truncated expansion method and extended homogeneous balance method. The basic idea is that the formal solution is assumed asu(x,t)=∑nm=0υ m(t)F m, F= e α(ξ+ξ 0) 1+ e α(ξ+ξ 0) which is then substituted into the given equation. It follows that the n will be determined and let the coefficients in the terms F with various powers be zero so that a integrable equation set is obtained. Thus, the exact solitude like solutions to the given equations are obtained.

关 键 词：广义变系数 孤子解 广义KDV方程 广义mKdV方程 截断展开法 延振齐次平衡法 非线性偏微分方程 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]