新(3+1)维KP方程的退化解与相互作用解  

Degeneration Behaviors of Solutions and Hybrid Solutions for the New(3+1)-Dimensional KP Equation

作　　者：郭艳凤[1] 崔静易 肖海军[1] 张景军 Guo Yanfeng;Cui Jingyi;Xiao Haijun;Zhang Jingjun(School of Mathematics and Physics,China University of Geosciences,Wuhan 430074;College of Data Science,Jiaxing University,Zhejiang Jiaxing 314001)

机构地区：[1]中国地质大学(武汉)数学与物理学院,武汉430074 [2]嘉兴大学数据科学学院,浙江嘉兴314001

出　　处：《数学物理学报（A辑）》2024年第6期1520-1536,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(11861013,11771183,12261053);广西科技基地与人才专项(AD21238019)

摘　　要：该文主要研究了由Wazwaz于2022年首次提出的新(3+1)维KP方程的非线性波解.基于Hirota双线性形式,利用模共振技术由N-孤子解得到P-呼吸解.然后,利用参数极限法,根据参数的特殊关系,对同宿呼吸解和N-孤子解进行退化得到了Lump解.最后,从N-孤子解的部分退化出发,研究了由呼吸解、孤子解和Lump解组成的相互作用解.该文通过可视化图形展示了这些解的动力学特性.We concentrate on the nonlinear wave solutions of the new(3+1)-dimensional KP equation,which was firstly proposed by Wazwaz in 2022.Based on the Hirota bilinear form,the P-breathing solutions are mainly obtained from the N-soliton solutions utilizing the module resonance technique.Then,using parameter limit approach,the Lump solutions are derived by degenerating behaviors of the homoclinic breathing solutions and N-soliton solutions on the basis of the special relations of parameters.In addition,from the partial degeneration of the N-soliton solutions,some hybrid solutions are investigated by the interaction solutions among the breathing,soliton and Lump solutions.

关 键 词：新 (3+1) 维 KP 方程 P -呼吸解 退化行为 Lump 解 相互作用解 

分 类 号：O175.29[理学—数学]