Liouville方程与其约化变换方程的精确解及ψ(ξ)展式法  

Exact Solutions of the Liouville Equation and Reduced Transformation Equation andψ(ξ)Expansion Method

作　　者：林府标 张千宏 LIN Fubiao;ZHANG Qianhong(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)

机构地区：[1]贵州财经大学数统学院,贵阳550025

出　　处：《吉林大学学报（理学版）》2021年第1期27-33,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11761018,11361012);贵州省科技计划基金(批准号:黔科合基础[2019]1051);贵州省科技厅科学技术基金(批准号:[2020]1Y008);贵州省教育厅青年科技人才成长项目(批准号:黔教合KY字[2017]150);2018年度贵州财经大学科研基金(批准号:2018XYB04);贵州财经大学创新探索及学术新苗项目(批准号:黔科合平台人才[2017]5736-020).

摘　　要：首先用广义tanh函数法和李群分析法,分别给出Liouville方程的显式新行波解和群不变解;其次用Liouville方程的约化变换方程及其精确解,构造一种有效求解非线性偏微分方程的ψ(ξ)展式法;最后用ψ(ξ)展式法给出Kawahara方程和(3+1)维Kadomtsev-Petviashvili方程的一些显式新行波解.Firstly,the explicit new travelling wave and group invariant solutions of the Liouville equation were given by using the method s of extended tanh-function and Lie group analysis,respectively.Secondly,theψ(ξ)expansion method for solving nonlinear partial differential equations was constructed by using the reduced transformation equation of the Liouville equation and its exact solutions.Finally,some explicit new travelling wave solutions of the Kawahara equation and(3+1)-dimensional Kadomtsev-Petviashvili equation were given by usingψ(ξ)expansion method.

关 键 词：LIOUVILLE方程 ψ(ξ)展式法 精确解 行波解 

分 类 号：O175.29[理学—基础数学]