(2+1)维Kadomtsev-Petviashvil方程的Weierstrass椭圆函数解  

Weierstrass Elliptic Function Solutions of the(2+1)-Dimensional Kadomtsev-Petviashvil Equation

作　　者：贾东婧 扎其劳[1,2] JIA Dong-jing;Zhaqilao(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematics,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]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（自然科学汉文版）》2023年第2期139-146,共8页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11861050,11261037);内蒙古自治区自然科学基金资助项目(2022ZD05,2020HL01010);内蒙古师范大学基本科研业务费专项资金资助项目(2022JBTD007,2022JBXC013);内蒙古师范大学研究生科研创新基金资助项目(CXJJB22010,CXJJS21119)。

摘　　要：利用Weierstrass型F-展开法求得(2+1)维Kadomtsev-Petviashvil(KP)方程的Weierstrass椭圆函数解。通过确定Weierstrass椭圆函数和Jacobi椭圆函数的转换公式,将Weierstrass椭圆函数解转化为Jacobi椭圆函数解。在椭圆模数取0或1极限的状态下,Jacobi椭圆函数解分别退化为三角函数解或双曲函数解。此外,通过绘制图像说明所得解的动态特性。The Weierstrass elliptic function solutions of the (2+1)-dimensional Kadomtsev-Petviashvil (KP) equation are obtained by using the Weierstrass F-expansion method in the paper. The solutions of Weierstrass elliptic function are transformed into Jacobi elliptic function solutions through the conversion formula between Weierstrass elliptic function and Jacobi elliptic function. When the elliptic modulus approaches to limit state of 0 or 1, Jacobi elliptic function solutions degenerate into trigonometric function solutions or hyperbolic function solutions correspondingly. In addition, some graphs are drawn to illustrate the dynamic characteristics of the obtained solutions.

关 键 词：Weierstrass椭圆函数解 Weierstrass型F-展开法 (2+1)维KP方程 

分 类 号：O175[理学—数学]