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The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations

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  • Wazwaz, Abdul-Majid

Abstract

The tanh method is applied to the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations. Solitons and periodic solutions for these equations are formally derived. The Painlevé property v=e±u will be employed to back up our analysis and to emphasize the effectiveness of the presented method.

Suggested Citation

  • Wazwaz, Abdul-Majid, 2005. "The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 55-63.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:1:p:55-63
    DOI: 10.1016/j.chaos.2004.09.122
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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. 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.
    4. 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. Zhou, Jiangrui & Zhou, Rui & Zhu, Shihui, 2020. "Peakon, rational function and periodic solutions for Tzitzeica–Dodd–Bullough type equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    4. Patra, A. & Baliarsingh, P. & Dutta, H., 2022. "Solution to fractional evolution equation using Mohand transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 557-570.
    5. Borhanifar, A. & Kabir, M.M. & Maryam Vahdat, L., 2009. "New periodic and soliton wave solutions for the generalized Zakharov system and (2+1)-dimensional Nizhnik–Novikov–Veselov system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1646-1654.
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    7. Lv, Xiumei & Lai, Shaoyong & Wu, YongHong, 2009. "An auxiliary equation technique and exact solutions for a nonlinear Klein–Gordon equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 82-90.
    8. (Benn)Wu, Xu-Hong & He, Ji-Huan, 2008. "EXP-function method and its application to nonlinear equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 903-910.

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