双(G/G',1/G)展开法求解(3+1)维mKdvZK方程和(3+1)维YTSF方程的新孤子解  

Double(G/G′,1/G)Expansion Method for Solving New Soliton Solutions of the(3+1)mKdvZK Equation and the(3+1)Dimensional YTSF Equation

作　　者：杨超 孙峪怀 韩梦娜 YANG Chao;SUN Yuhuai;HAN Mengna(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2024年第1期1-9,共9页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目“带奇异势的非线性Schrodinger方程解的渐近行为研究”(12071323)。

摘　　要：研究(3+1)维修正Korteweg-devries-Zakharov-Kuznestsov方程和(3+1)维Yu-Toda-Sassa-Fukuymama方程的解。首先利用行波变换和代入变换将(3+1)维mKdvZKE和(3+1)维YTSFE转化为常微分方程,而后选择双(G/G’,1/G)展开法得到多个与现有的文献不同的精确解。本方法丰富了(3+1)维修正Korteweg-devries-Zakharov-Kuznestsov方程和(3+1)维Yu-Toda-Sassa-Fukuymama方程的解,说明所用方法和过程对构造非线性演化方程的精确解具有科学性和通用性。In the paper,we study the(3+1)-maintained positive Korteweg-devries-Zakharov-Kuznestsov(mKdvZKE)equations and(3+1)-dimensional Yu-Toda-Sassa-Fukuymama(YTSFE)equations,which have a wide background of application and important significance in nonlinear science and engineering.The(3+1)-dimensional mKdvZKE and(3+1)-dimensional YTSFE are firstly transformed into ordinary differential equations by applying the travelling wave transformation and the substitution transformation,and then the new exact solutions of the two equations are obtained by choosing the double(G/G′,1/G)expansion method.As examples,the method is applied to solutions for kink,soliton wave,periodic function,trigonometric function,etc.The method enriches the solutions of(3+1)-dimensional modified Korteweg-devries-Zakharov-Kuznestsov(mKdvZKE)equations and(3+1)-dimensional Yu-Toda-Sassa-Fukuymama(YTSFE)equations,which demonstrates the scientificity and universality of the method in solving the new exact solutions of the nonlinear evolution equations.

关 键 词：双(G/G’ 1/G)展开法 修正Korteweg-devries-Zakharov-Kuznestsov方程 Yu-Toda-Sassa-Fukuymama方程 精确解 

分 类 号：O175.29[理学—数学]