(2+1)维KdV方程的孤子解和新Wronskian行列式解  

Soliton Solutions and New Wronskian Determinant Solutions of the (2+1) Dimensional KdV Equation

作　　者：郭婷婷[1] 

机构地区：[1]山西大学商务学院,山西太原030031

出　　处：《中北大学学报（自然科学版）》2015年第2期118-121,125,共5页Journal of North University of China(Natural Science Edition)

基　　金：山西大学商务学院科研项目(2013025)

摘　　要：对(2+1)维KdV方程进行研究,基于Wronskian行列式和Hirota双线性方法,应用行列式的性质,给出(2+1)维KdV方程Wronskian表示的孤子解.利用Hirota方法,在(2+1)维KdV方程经典孤子解的基础上,得出方程新的单孤子解.通过观察Wronskian行列式元素的特征并分析所满足的色散关系,重新定义行列式元素,利用Hirota方法和Wronskian技巧,构造出新的2 N阶Wronskian行列式解,并应用行列式恒等式说明双线性型的孤子方程有Wronskian解.通过直接计算证明了两种新解的一致性.The （2＋1）dimensional KdV equation was researched,based on Wronskian determinant and Hirota method,soliton solutions of the （2 ＋1）dimensional KdV equation in the Wronskian form were derived by using determinant properties.On the basis of the classical soliton solutions of the （2＋1）di-mensional KdV equation,the new one-soliton solution was obtained through Hirota method.Based on observing the features of the Wronskian determinant elements and analyzing the dispersion relation,de-terminant elements were then re-defined and new 2N-order Wronskian determinant solutions were con-structed by Hirota method and Wronskian technique.It is shown that the Wronskian solutions are the solutions of the bilinear form of the soliton equations by determinant identical equation.The consistency of the two kinds of solutions was proved by calculation.

关 键 词：HIROTA 方法 (2+1)维 KDV 方程 孤子解 WRONSKIAN 行列式解 

分 类 号：O129.35[理学—数学]