约化的(3+1)维Hirota方程的呼吸波解、lump解和半有理解

Breather Wave Solutions,Lump Solutions and Semi-Rational Solutions of a Reduced(3+1)Dimensional Hirota Equation

该文利用长波极限方法研究了(3+1)维Hirota方程在维数约化z=x下的精确解.首先利用贝尔多项式构造了其双线性形式.基于双线性形式,对N-孤子解做某些参数约束,获得了n-阶呼吸波解.其次,利用长波极限方法获得了高阶lump波解.最后导出了一阶,二阶lump波解分别与单孤子解的混合解,即半有理解.所有得到的解都通过Maple软件进行物理特征分析.

In this paper,the long wave limit method is used to study the exact solutions of the(3+1)dimensional Hirota equation under dimensional reduction z=x.First,the bilinear form is constructed by using Bell polynomials.Based on the bilinear form,the n-order breather wave solutions are obtained under some parameter constraints on the N-order soliton solution.Secondly,by using the long wave limit method,high order lump wave solutions are obtained.Finally,the combined solutions of the first-order,second-order lump wave solutions and single solitary wave solutions are derived,i.e.semi-rational solutions.All the obtained solutions were analyzed with Maple software for physical characteristics.