摘要
基于整数阶辅助方程法的相关结论,给出了分数阶Riccati方程的包含广义双曲函数解和广义三角函数解的Mittag-Leffler函数新解、Bäcklund变换和解的非线性叠加公式.在此基础上,借助符号计算系统Mathematica,构造了分数阶KdV-mKdV方程、分数阶(3+1)维Zakharov-Kuznetsov方程和分数阶Boussinesq方程的无穷序列新解.
Based on the relevant conclusions of the integer order auxiliary equation method,new Mittag-Leffler function solutions of the fractional Riccati equation are given,including generalized hyperbolic function solution and generalized trigonometric function solution,the Bäcklund transformation and nonlinear superposition formula of solution for the equation are obtained.On this basis,with the help of symbolic computing system Mathematica,new infinite sequence solutions of fractional KdV-mKdV equation,fractional(3+1)-dimensional Zakharov-Kuznetsov equation and fractional Boussinesq equation are constructed.
作者
伊丽娜
扎其劳
套格图桑
YI Lina;ZHA Qilao;Taogetusang(College of Mathematical Science,Inner Mongolia Normal University,Huhhot 010022,China;Center for Applied Mathematics of Inner Mongolia Autonomous Regin,Huhhot 010022,China;Key Laboratory of In nite-Dimensional Hamiltonian System and Its Algorithm Application,Ministry of Education,Huhhot 010022,China)
出处
《应用数学》
北大核心
2024年第4期1121-1132,共12页
Mathematica Applicata
基金
国家自然科学基金(11361040,12361052)
内蒙古自治区自然科学基金(2024MS01003)
内蒙古师范大学基本科研业务费专项资金资助项目(2022JBZD011)。
