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Exact Traveling Wave Solutions for a Nonlinear Evolution Equation of Generalized Tzitzéica‐Dodd‐Bullough‐Mikhailov Type

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  • Weiguo Rui

Abstract

By using the integral bifurcation method, a generalized Tzitzéica‐Dodd‐Bullough‐Mikhailov (TDBM) equation is studied. Under different parameters, we investigated different kinds of exact traveling wave solutions of this generalized TDBM equation. Many singular traveling wave solutions with blow‐up form and broken form, such as periodic blow‐up wave solutions, solitary wave solutions of blow‐up form, broken solitary wave solutions, broken kink wave solutions, and some unboundary wave solutions, are obtained. In order to visually show dynamical behaviors of these exact solutions, we plot graphs of profiles for some exact solutions and discuss their dynamical properties.

Suggested Citation

  • Weiguo Rui, 2013. "Exact Traveling Wave Solutions for a Nonlinear Evolution Equation of Generalized Tzitzéica‐Dodd‐Bullough‐Mikhailov Type," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:395628
    DOI: 10.1155/2013/395628
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    References listed on IDEAS

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    1. Khani, F., 2009. "Analytic study on the higher order Ito equations: New solitary wave solutions using the Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2128-2134.
    2. Weiguo Rui & Yao Long, 2012. "Integral Bifurcation Method together with a Translation‐Dilation Transformation for Solving an Integrable 2‐Component Camassa‐Holm Shallow Water System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Weiguo Rui & Yao Long, 2012. "Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-21, December.
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