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

Quting Chen; Yadong Shang; Quting Chen; Yadong Shang

doi:10.3934/math.2019.2.231

AIMS Mathematics

2019, Volume 4, Issue 2: 231-241. doi: 10.3934/math.2019.2.231

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Research article

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

Quting Chen ,
Yadong Shang ^,

School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong, 510006, P.R. China

Received: 29 November 2018 Accepted: 22 February 2019 Published: 07 March 2019
MSC : 35L70, 35Q58

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.
- similarity reductions,
- direct method,
- short pulse equation,
- exact solution,
- the method of undetermined coefficients
Citation: Quting Chen, Yadong Shang. Direct similarity reductions and new exact solutions of the short pulse equation[J]. AIMS Mathematics, 2019, 4(2): 231-241. doi: 10.3934/math.2019.2.231

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Abstract

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.

References

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