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Analytical and Multishaped Solitary Wave Solutions for Extended Reduced Ostrovsky Equation

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  • Ben-gong Zhang

Abstract

We present the analytical and multishaped solitary wave solutions for extended reduced Ostrovsky equation (EX‐ROE). The exact solitary (traveling) wave solutions are expressed by three types of functions which are hyperbolic function solution, trigonometric function solution, and rational solution. These results generalized the previous results. Multishape solitary wave solutions such as loop‐shaped, cusp‐shaped, and hump‐shaped can be obtained as well when the special values of the parameters are taken. The (G′/G)‐expansion method presents a wide applicability for handling nonlinear partial differential equations.

Suggested Citation

  • Ben-gong Zhang, 2013. "Analytical and Multishaped Solitary Wave Solutions for Extended Reduced Ostrovsky Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:670847
    DOI: 10.1155/2013/670847
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    References listed on IDEAS

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    1. Ming Song & Bouthina S. Ahmed & Anjan Biswas, 2013. "Topological Soliton Solution and Bifurcation Analysis of the Klein-Gordon-Zakharov Equation in -Dimensions with Power Law Nonlinearity," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, March.
    2. Stepanyants, Y.A., 2006. "On stationary solutions of the reduced Ostrovsky equation: Periodic waves, compactons and compound solitons," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 193-204.
    3. Ming Song & Bouthina S. Ahmed & Anjan Biswas, 2013. "Topological Soliton Solution and Bifurcation Analysis of the Klein‐Gordon‐Zakharov Equation in (1 + 1)‐Dimensions with Power Law Nonlinearity," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Ming Song, 2012. "Application of Bifurcation Method to the Generalized Zakharov Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-8, November.
    5. Ming Song, 2012. "Application of Bifurcation Method to the Generalized Zakharov Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Parkes, E.J., 2007. "Explicit solutions of the reduced Ostrovsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 602-610.
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    Cited by:

    1. Hongwei Yang & Qingfeng Zhao & Baoshu Yin & Huanhe Dong, 2013. "A New Integro‐Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Yazhou Shi & Xiangpeng Li & Ben-gong Zhang, 2018. "Traveling Wave Solutions of Two Nonlinear Wave Equations by (G′/G)‐Expansion Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).

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