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A generalized auxiliary equation method and its applications

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Abstract

In this paper, a generalized auxiliary equation method with the aid of the computer symbolic computation system Maple is proposed to construct more exact solutions of nonlinear evolution equations, namely, the higher-order nonlinear Schrödinger equation, the Whitham–Broer–Kaup system, and the generalized Zakharov equations. As a result, some new types of exact travelling wave solutions are obtained, including soliton-like solutions, trigonometric function solutions, exponential solutions, and rational solutions. The method is straightforward and concise, and its applications are promising.

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Authors and Affiliations

  1. Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt

    M. A. Abdou

  2. Science Department, Faculty of Education for Girls, Bisha, Saudi Arabia

    M. A. Abdou

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  1. M. A. Abdou
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Correspondence to M. A. Abdou.

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Abdou, M.A. A generalized auxiliary equation method and its applications. Nonlinear Dyn 52, 95–102 (2008). https://doi.org/10.1007/s11071-007-9261-y

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  • DOI: https://doi.org/10.1007/s11071-007-9261-y

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