变系数Pavlov方程的李对称分析、精确解和守恒律  

Lie Symmetry Analysis,Exact Solutions and Conservation Laws to the Variable Efficients Pavlov Equation

作　　者：胡玉茹 张峰 辛祥鹏[1] HU Yu-ru;ZHANG Feng;XIN Xiang-peng(School of Mathematical Sciences,Liaocheng University,Liaocheng 252000,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252000

出　　处：《安徽师范大学学报（自然科学版）》2022年第4期307-317,386,共12页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(11505090).

摘　　要：首次将Pavlov方程扩展为一个新的变系数方程。运用李群分析法研究了变系数Pavlov方程的对称,得到了方程的无穷小生成元及单参数变换群,在此基础上,推导出变系数Pavlov方程的一维子代数最优系统。通过相似约化,将(2+1)维变系数Pavlov方程约化为(1+1)维偏微分方程,进而通过行波变换构造了变系数Pavlov方程新的精确解,包括暗孤子解、周期解、二孤子相互作用解和扭结周期波相互作用解等。最后对变系数Pavlov方程的自伴随性进行分析,得到了该方程的守恒律。In this paper,the Pavlov equation is extended to a new variable coefficients equation for the first time.The symmetry of the variable coefficients Pavlov equation is studied using Lie symmetry analysis,and the infinitesimal generators of the equation and the one-parameter transformation groups are obtained,on the basis of which the one-dimensional subalgebras optimal system of the variable coefficients Pavlov equation is obtained.The(2+1)-dimensional Pavlov equation is reduced to the(1+1)-dimensional partial differential equation by similarity reductions,and then new exact solutions of the variable coefficients Pavlov equation are constructed by traveling wave transform,including dark soliton solutions,periodic solutions,two-soliton interaction solutions and kinked solutions with periodic wave.Finally,the nonlinear self-adjointness of the variable coefficients Pavlov equation is analyzed to obtain the conservation laws for the equation.

关 键 词：变系数Pavlov方程 李对称分析 最优系统 精确解 守恒律 

分 类 号：O175.2[理学—数学]