达布变换与(2+1)维Gardner方程的新解(英文)  

Darboux Transformation and New Solutions for the (2+1)-dimensional Gardner Equation

作　　者：扎其劳[1] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《内蒙古大学学报（自然科学版）》2010年第2期132-137,共6页Journal of Inner Mongolia University：Natural Science Edition

基　　金：supported by the Natural Science Foundation of Inner Mongolia(Grant No.2009MS0108);the Natural Science Foundation(Grant No ZRYB08017);the Initial Fundingof Scientific Research Project for Ph.D of Inner Mongolia Normal University~~

摘　　要：近期,耿献国和曹策问将(2+1)维Gardner方程分解到两个(1+1)维孤子方程.本文计算出这两个(1+1)维孤子方程的Lax对,并利用Lax对的规范变换构造了该(1+1)维孤子方程的新达布变换.应用达布变换和分解获得了(2+1)维Gardner方程的一些新显式解,其中包括多孤子解.Recently, the （2 ＋ 1）-dimensional Gardner equation was decomposed into two known （1 ＋ 1）-dimensional soliton equations by Geng and Cao. In this paper,the Lax pairs of the two （1 ＋ 1）-dimensional soliton equations are derived. A new Darboux transformation of the two known （1 ＋ 1）-dimensional soliton equations is constructed with the heap of a gauge transformation of the Lax pairs. As an application of the Darboux transformation and the decomposition, some new explicit solutions of the （2 ＋ 1）-dimensional Gardner equation are obtained, which including multi-soliton solutions.

关 键 词：达布变换 孤子解 (2+1)维Gardner方程 

分 类 号：O175.2[理学—数学]