受迫耗散Boussinesq方程的可积性质和孤波解的探讨  

The Integrable Properties And Solitary Wave Solution for a Forced Dissipative Bousssineq Equation

作　　者：孟祥花[1] 许晓革[1] 

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《数学的实践与认识》2014年第17期301-305,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61072145);北京市优秀人才项目(2013D005007000003)

摘　　要：考虑到耗散效应和地形外力,Rossby波的振幅可由受迫耗散Boussinesq方程来描述.当包含这两项时,模型比较复杂,不具有Painleve性质.通过将模型双线性化,双线性方法是一个可寻找孤波解和B(a|¨)cklund变换的方法.通过截断的Painleve展开式,得到了将方程双线性化的合适的因变量变换.然后得到了受迫耗散Boussinesq方程的单孤波解和B(a|¨)cklund变换.Considering the dissipation effect and topographic forcing, the Rossby waves amplitude can be modeled by a forced dissipative Boussinesq equation. Including both terms, the modeling equation is complicated and doesn＇t possess the Painleve property. The bilinear method is an approach for seeking soliton solntions and Backlund transformation by bilinearizing the investigated equation. Through the truncated Painleve expansion, the suitable dependent; variable transformation for the forced dissipative Boussinesq equation is found to bilinearize the equation. And then, the one-solitary wave solution and Backlund transformation for the equation are obtained.

关 键 词：受迫耗散Boussinesq方程 PAINLEVE性质 双线性方程 孤波解 BACKLUND变换 

分 类 号：O175.29[理学—数学]