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Generalized forms of the phi-four equation with compactons, solitons and periodic solutions

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  • Wazwaz, Abdul-Majid

Abstract

In this paper we study two generalized forms of the phi-four equation. Compactons: solitons with the absence of infinite wings, conventional solitons: nonlinear localized waves with infinite support, solitary patterns solutions having infinite slopes or cusps, and plane periodic solutions are developed. The sine–cosine ansatz can be fruitfully employed to develop these physical solutions. The qualitative change in the physical structure of the obtained solutions is shown to depend mainly on the exponent of the wave function u(x,t), positive or negative, and on the coefficient of the term (un)xx as well.

Suggested Citation

  • Wazwaz, Abdul-Majid, 2005. "Generalized forms of the phi-four equation with compactons, solitons and periodic solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(5), pages 580-588.
    • Handle: RePEc:eee:matcom:v:69:y:2005:i:5:p:580-588
    DOI: 10.1016/j.matcom.2005.03.018
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    References listed on IDEAS

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    1. Wazwaz, A.M., 2001. "A study of nonlinear dispersive equations with solitary-wave solutions having compact support," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(3), pages 269-276.
    2. Wazwaz, Abdul-Majid, 2003. "An analytic study of compactons structures in a class of nonlinear dispersive equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(1), pages 35-44.
    3. Ismail, M.S. & Taha, T.R., 1998. "A numerical study of compactons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(6), pages 519-530.
    4. Wazwaz, Abdul-Majid & Taha, Thiab, 2003. "Compact and noncompact structures in a class of nonlinearly dispersive equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(1), pages 171-189.
    5. Wazwaz, A.M., 2002. "General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations mK(n,n) in higher dimensional spaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(6), pages 519-531.
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    Cited by:

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    2. Kumar, Vineesh & Patel, Arvind, 2020. "Construction of the soliton solutions and modulation instability analysis for the Mel’nikov system," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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