YTSF方程的Lie点对称群及其非行波动力学行为  

Lie Point Symmetry Group of the YTSF Equations and Its Non-traveling Dynamical Behavior

作　　者：陈炜 鲜大权[1] 蒲志强 CHEN Wei;XIAN Daquan;PU Zhiqiang(School of Mathematics and Physics,Southwest University of Science and Technology,Mianyang 621010,Sichuan;School of Mathematics and Physics,Mianyang Teachers’College,Mianyang 621000,Sichuan)

机构地区：[1]西南科技大学数理学院,四川绵阳621010 [2]绵阳师范学院数理学院,四川绵阳621010

出　　处：《四川师范大学学报（自然科学版）》2023年第6期748-755,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11771414);中国高校产学研创新基金(2020ITA02019)。

摘　　要：获得Yu-Toda-Sasa-Fukuyama方程(简称为YTSF方程)含5个任意函数的Lie对称,对YTSF方程作了3种情况的对称约化,分别采用Jacobi椭圆函数展开法、CRE展开法和变量分离法求解3个对称约化方程,得到非行波周期解、孤子解、相容Riccati方程解与和式变量分离解,结合数字技术分析YTSF方程的动力学局域激发模式.这些结果展示了该方程可积性和动力学特性的多样性,实证了多种非线性数学方法有机结合的有效性.In this paper,we obtain Lie symmetry with five arbitrary functions about t of YTSF equation and a symmetric reduction of the three cases is constructed for the equation.The Jacobi elliptic expansion method,CRE expansion method and separation of variables method are applied to the three symmetry-reduction equations to find the non-traveling wave periodic solution,soliton wave solution,compatible Riccati equation solution and variable separation solution in summation form.The dynamics local excitation modes of the equation are analyzed in combination with digital techniques.These results demonstrate the integrability of the YTSF equation and diversity of dynamical properties and demonstrate the effectiveness of a combination of multiple nonlinear mathematical methods.

关 键 词：YTSF方程 LIE群 CRE展开法 变量分离 非行波精确解 

分 类 号：O175.2[理学—数学]