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Approximate Damped Oscillatory Solutions for Generalized KdV‐Burgers Equation and Their Error Estimates

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  • Weiguo Zhang
  • Xiang Li

Abstract

We focus on studying approximate solutions of damped oscillatory solutions of generalized KdV‐Burgers equation and their error estimates. The theory of planar dynamical systems is employed to make qualitative analysis to the dynamical systems which traveling wave solutions of this equation correspond to. We investigate the relations between the behaviors of bounded traveling wave solutions and dissipation coefficient, and give two critical values λ1 and λ2 which can characterize the scale of dissipation effect, for right and left‐traveling wave solution, respectively. We obtain that for the right‐traveling wave solution if dissipation coefficient α ≥ λ1, it appears as a monotone kink profile solitary wave solution; that if 0

Suggested Citation

  • Weiguo Zhang & Xiang Li, 2011. "Approximate Damped Oscillatory Solutions for Generalized KdV‐Burgers Equation and Their Error Estimates," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:807860
    DOI: 10.1155/2011/807860
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    Cited by:

    1. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Weiguo Rui, 2014. "Exact Solutions of a High‐Order Nonlinear Wave Equation of Korteweg‐de Vries Type under Newly Solvable Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(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, John Wiley & Sons, vol. 2012(1).
    4. Xianbin Wu & Weiguo Rui & Xiaochun Hong, 2013. "A Generalized KdV Equation of Neglecting the Highest‐Order Infinitesimal Term and Its Exact Traveling Wave Solutions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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