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

Weiguo Zhang and Xiang Li

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

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

Date: 2011
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https://doi.org/10.1155/2011/807860

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:807860

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