Research article

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

  • 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.

    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

    Related Papers:

  • 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.


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