扩展的同宿检验法与(3+1)维广义KP方程的非行波解  

Extended homoclinic test approach and non-traveling wave solutions of(3+1)dimensional generalized KP equation

作　　者：郑筱筱 段风霜 陈思远 张舒涵 ZHENG Xiaoxiao;DUAN Fengshuang;CHEN Siyuan;ZHANG Shuhan(School of Mathematical Sciences,Qufu Normal University,273165,Qufu,Shandong;College of Mathematics,Jilin University,130012,Changchun,Jilin,PRC)

机构地区：[1]曲阜师范大学数学科学学院,山东省曲阜市273165 [2]吉林大学数学学院,吉林省长春市130012

出　　处：《曲阜师范大学学报（自然科学版）》2022年第3期95-102,共8页Journal of Qufu Normal University(Natural Science)

基　　金：山东省自然科学基金(ZR2018BA016,ZR2020MA013);山东省大学生创新创业训练计划项目(S202010446095,S202110446093).

摘　　要：扩展的同宿检验法是求解非线性偏微分方程精确解非常有效的方法.该文将扩展的同宿检验法与分离变量方法相结合,探索(3+1)维广义KP方程的非行波精确解.借助数学软件工具,讨论了4种情形下的非行波精确解.进而,通过分析系数在实数域、复数域中的取值情况,得到了(3+1)维广义KP方程15种类型的精确非行波解.The extended homoclinic test approach is an effective method to get exact solutions of nonlinear partial differential equation.In this paper,the extended homoclinic test approach and variable separation method are used to explore non-traveling wave solutions of(3+1)dimensional generalized KP equation.With the help of mathematical software,the exact non-traveling solutions in four cases are discussed.Then,by analyzing the value of coefficients in real number field and complex number field,fifteen types of exact non-traveling wave solutions of(3+1)dimensional generalized KP equation are obtained.

关 键 词：扩展的同宿检验法 分离变量方法 (3+1)维广义KP方程 非行波解 

分 类 号：O175.2[理学—数学]