Direct similarity reductions and new exact solutions of the short pulse equation

AIMS Mathematics

Quting Chen¹  Yadong Shang¹ 

[1] School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong, 510006, P.R. China;

关键词: similarity reductions;    direct method;    short pulse equation;    exact solution;    the method of undetermined coefficients;   

DOI  :  10.3934/math.2019.2.231

来源: DOAJ

【 摘 要 】

In this paper, we present some similarity reductions of the short pulse equation(SPE) based on the direct similarity reduction method proposed by Clarkson and Kruskal. These similarity reductions have a more general form than those obtained by using the Lie group method. Especially, we obtain one new similarity reduction which can not be obtained by Lie group method. Furthermore, we derive one new exact analytic solutions by the method of undetermined coefficients.

【 授权许可】

Unknown