修正Kadomtsev-Petviashvili方程的分解及其孤子解  

On the Decomposition of the Modified Kadomtsev-Petviashvili Equation and Its Soliton Solutions

作　　者：李权[1] 扎其劳[2,3] LI Quan;Zhaqilao(Department of Mathematics and Computer Science,Hetao College,Bayannur 015008,Inner Mongolia,China;College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center of Applied Mathematics,Hohhot 010022,China)

机构地区：[1]河套学院数学与计算机系,内蒙古巴彦淖尔015008 [2]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [3]内蒙古自治区应用数学中心,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学版）》2022年第4期331-335,F0002,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11861050);内蒙古自治区自然科学基金资助项目(2020LH01010);河套学院科学研究资助项目(HYZY201935)。

摘　　要：把(2+1)维修正Kadomtsev-Petvishivili方程分解成Kaup-Newell族的两个(1+1)维孤子方程组。利用Kaup-Newell族的线性谱问题,为这两个(1+1)维孤子方程组构造了新的Darboux变换。应用Darboux变换和分解式,求得修正Kadomtsev-Petvishivili方程的一些孤子解。The(2+1)dimensional modified Kadomtsev-Petvishivili equation is decomposed into two known(1+1)dimensional soliton systems in the Kaup-Newell hierarchy.A new N-fold Darboux transformation of the two known(1+1)dimensional soliton systems is derived with the help of a gauge transformation of the Kaup-Newell hierarchy.As an application of the Darboux transformation and the decomposition,some soliton solutions of the(2+1)dimensional modified Kadomtsev-Petvishivili equation are presented in the paper.

关 键 词：分解 孤子解 DARBOUX变换 修正Kadomtsev-Petvishivili方程 

分 类 号：O175.2[理学—数学]