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

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.