受外力影响下变系数广义五阶KdV类模型N-孤子解析解及其应用  

Analytic N-soliton Solutions for the Variable-coefficient Generalized Fifth-order KdV-like Model with External Force and Application

作　　者：孙福伟[1,2] 王敏[2] 

机构地区：[1]北京航空航天大学航空科学与工程学院,北京100191 [2]北方工业大学理学院,北京100144

出　　处：《数学的实践与认识》2013年第9期256-267,共12页Mathematics in Practice and Theory

摘　　要：借助计算机符号运算,研究了流体力学和等离子体中由外力和环境所导致的高阶非线性因素产生的变系数广义五阶KdV类模型.通过Hirota方法,得到了该模型的双线性形式以及高阶非线性项和高阶色散项之间的变系数函数的约束条件.求出了该模型解析的单孤子解、双孤子解、三孤子解,以及N-孤子解的解析表达式.通过给出的多孤子间传播状态的仿真图像,分析得出在不同的环境下受外力和变系数函数的影响下,孤子间相互作用发生了很大变化.通过孤子的不同图形详细解释了其传播过程中具有的相关性质,从而可以帮助人们更进一步了解流体力学和等离子体物理的一些物理过程和现象.With the help of symbolic computation, this paper investigates the variable- coefficient generalized fifth-order KdV-like model with different external force in certain flu- ids. The bilinear form for this model is obtained with the aid of Hirota＇s method. And the constraint conditions of the high-order nonlinear items and high-order dispersive items for this model are derived. Based on the obtained bilinear form, some of its one-, two-, three-soliton and other interesting solutions are derived. Analytic N-soliton solution expression for the variable-coefficient generalized fifth-order KdV-like model is constructed. Relevant properties of multiple-soliton with influence of different external force and the high-order nonlinear fac- tors are graphically illustrated, which might be helpful to understand more deeply into some physical processes and phenomena in certain fluids and plasmas.

关 键 词：变系数广义五阶KdV类模型 HIROTA方法 解析的N-孤子解 符号计算 

分 类 号：O175[理学—数学]