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Exact solutions of some nonlinear partial differential equations using functional variable method

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Abstract

The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation and the higher-order nonlinear Schrödinger equation. By using this useful method, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. It is shown that the proposed method is effective and general.

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Authors and Affiliations

  1. Department of Mathematics, Islamic Azad University, Dezful Branch, Dezful, Iran

    A NAZARZADEH

  2. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    M ESLAMI

  3. Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran

    M MIRZAZADEH

Authors
  1. A NAZARZADEH
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  2. M ESLAMI
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  3. M MIRZAZADEH
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Correspondence to M MIRZAZADEH.

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NAZARZADEH, A., ESLAMI, M. & MIRZAZADEH, M. Exact solutions of some nonlinear partial differential equations using functional variable method. Pramana - J Phys 81, 225–236 (2013). https://doi.org/10.1007/s12043-013-0565-9

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  • DOI: https://doi.org/10.1007/s12043-013-0565-9

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