两类非线性方程(组)的对称约化和精确解  

Symmetry Reduction and Exact Solution of Two Kinds of Nonlinear Equation System

作　　者：孙世飞 李雪霞 刘汉泽[1] SUN Shi-fei;LI Xue-xia;LIU Han-ze(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：《聊城大学学报（自然科学版）》2020年第4期8-13,共6页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目(11171041)资助。

摘　　要：利用直接对称的方法研究了Cubic-非线性Schrodinger(CNS)方程和非线性Schr?dinger(NLS)方程两类非线性方程,得到了两类不同阶的Schrodinger方程的对称和约化方程,借助对称得到了包括行波解在内的多个精确解,并对两类方程的高阶约化方程进行分析讨论从而得到了幂级数形式的新精确解。In this paper,two kinds of Schrodinger equations of CNS and NLS are studied by direct symmetry method,the symmetric and reduced equations of the two kinds of equations are obtained,and many exact solutions including traveling wave solutions are obtained by the symmetries and reduced equations,then the exact solutions of the power series form are obtained by analyzing the higher-order reduced equations of the two kinds of equations.

关 键 词：非线性偏微分方程组 李点对称 精确解 

分 类 号：O175.2[理学—数学]