非线性弦振动方程的最优系统、不变解及守恒律  

Optimal System,Invariant Solutions and Conservation Laws of the Nonlinear Vibrating String Equation

作　　者：张寒 ZHANG Han(School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《滨州学院学报》2022年第2期63-68,共6页Journal of Binzhou University

基　　金：山东省自然科学基金项目(ZR2021MA084)。

摘　　要：应用经典的李群方法研究非线性弦振动方程,分析了该方程的李对称和一维子代数的最优系统。通过相似约化,得到非线性弦振动方程的精确解,同时利用幂级数展开法得到了幂级数解。最后讨论了非线性弦振动方程的守恒律。The classical Lie group method is applied to the nonlinear vibrating string equation,then the Lie symmetries and the optimal system of one-dimensional subalgebras of the equation are analyzed.The exact solutions of nonlinear vibrating string equation are investigated by similarity reduction.Meanwhile,the power series solution is obtained by power series expansion method.Finally,the conservation laws of nonlinear vibrating string equation are discussed.

关 键 词：李对称分析 非线性弦振动方程 最优系统 精确解 守恒律 

分 类 号：O175[理学—数学]