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The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations

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  • Wazwaz, Abdul-Majid

Abstract

This paper is devoted to studying the KP–BBM and the ZK–BBM equations. The extended tanh method is used to conduct the analysis. The KP–BBM and the ZK–BBM equations give rise to compactons solutions: solitons with the absence of infinite tails, solitons: nonlinear localized waves of infinite support, solitary patterns solutions having infinite slopes or cusps, and plane periodic solutions. The work confirms the power of the proposed method.

Suggested Citation

  • Wazwaz, Abdul-Majid, 2008. "The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1505-1516.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:5:p:1505-1516
    DOI: 10.1016/j.chaos.2007.01.135
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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.
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    Cited by:

    1. Estévez, P.G. & Kuru, Ş. & Negro, J. & Nieto, L.M., 2009. "Travelling wave solutions of the generalized Benjamin–Bona–Mahony equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2031-2040.
    2. Bekir, Ahmet, 2009. "The tanh–coth method combined with the Riccati equation for solving non-linear equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1467-1474.
    3. Nizovtseva, I.G. & Galenko, P.K. & Alexandrov, D.V., 2017. "Traveling wave solutions for the hyperbolic Cahn–Allen equation," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 75-79.

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