(2+1)维广义柱Kadomtsev-Petviashvilli方程的Painlevé分析及精确解  

PainlevéAnalysis and Exact Solutions to the(2+1)-Dimensional Kadomtsev-Petviashvilli Equations

作　　者：唐晓苓 刘汉泽[1] TANG Xiao-ling;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3期1-5,共5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：将Painlevé分析的WTC方法应用到高维变系数方程中,并以(2+1)维广义变系数KP方程为例,得到精确解;首先对(2+1)维广义柱Kadomtsev-Petviashvilli方程进行Painlevé分析,确定Painlevé展开式,其次确定共振点,验证共振点,进行相容性分析,最后给出新形式的精确解及其解的图像,在此基础上,再利用G′/G展开法,得到该方程新的一般形式的精确解,并讨论特殊情况下该方程的一组特解,扩大解的范围,使方程的解更加完善.This article with Painlevéanalysis of the WTC method is first applied to the high dimensional equation with variable coefficients,and the(2+1)dimensional Kadomtsev-Petviashvilli equation as an example,For the(2+1)dimensional generalized column Kadomtsev-Petviashvilli equation Painlevéanalysis,determine the Painlevéexpansion,determine the resonance point,verify the resonance point,Secondly compatibility analysis,get the equation of Painlevéproperties,And give a picture of the exact solution of the new form and its solution,On this basis,the G′/G-expansion method is used to obtain the accurate solution of the new general form of the equation,and to discuss a group of special solutions of the equation in special cases to expand the range of solutions and improve the solution of the equation.

关 键 词：(2+1)维广义柱Kadomtsev-Petviashvilli方程 PAINLEVÉ分析 G′/G展开法 精确解 

分 类 号：O175.2[理学—数学]