维数约化的弱耦合KP-Boussinesq方程的lump解和有理解  

Lump and rational solutions to the dimensionally reduced weakly coupled KP-Boussinesq equation

作　　者：刘袁 汪一航[1] LIU Yuan;WANG Yihang(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2021年第5期43-48,共6页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(11775121,11435005).

摘　　要：利用Z_(m)-KP方程族,构造了一个新的弱耦合广义KP-Boussinesq方程.基于Hirota双线性方法,通过构造对称的半正定矩阵,得到维数约化情形下的lump解和有理解,并对其基本特征进行了研究.另外,通过对有理解的数值分析研究了其动力学性质.By taking advantage of Z_(m)-KP hierarchy,a new weakly coupled generalized KP-Boussinesq equation is constructed.Based on the Hirota bilinear method and constructions to the symmetric positive semi-definite matrix,the lump and rational solutions are obtained in the dimensionally reduced cases.Characteristics of solutions are also investigated.The dynamic properties of rational solutions are also derived using the numerical analysis.

关 键 词：弱耦合广义KP-Boussinesq方程 双线性方程 lump解 有理解 数值分析 

分 类 号：O175[理学—数学]