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On the exact solutions of nonlinear evolution equations by the improved \(\tan (\varphi /2)\)-expansion method

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Abstract

In this paper, the improved \(\tan (\varphi /2)\)-expansion method (ITEM) is proposed to obtain more general exact solutions of the nonlinear evolution equations (NLEEs). This method is applied to the generalised Hirota–Satsuma coupled KdV (HScKdV) equation and \((2+1)\)-dimensional Nizhnik–Novikov–Veselov (NNV) system. We have obtained four types of solutions of these equations such as hyperbolic, trigonometric, exponential and rational functions as an advantage of this method. These solutions include solitons, rational, periodic and kink solutions. Moreover, modulation instability is used to establish stability of the obtained solutions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, 16059 , Bursa, Turkey

    Yeşim Sağlam Özkan & Emrullah Yaşar

Authors
  1. Yeşim Sağlam Özkan
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  2. Emrullah Yaşar
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Correspondence to Yeşim Sağlam Özkan.

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Dedicated to Prof. Mehmet Cagliyan on the occasion of his 70th birthday.

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Özkan, Y.S., Yaşar, E. On the exact solutions of nonlinear evolution equations by the improved \(\tan (\varphi /2)\)-expansion method. Pramana - J Phys 94, 37 (2020). https://doi.org/10.1007/s12043-019-1883-3

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  • DOI: https://doi.org/10.1007/s12043-019-1883-3

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