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Existence of Solitary Waves in a Perturbed KdV-mKdV Equation

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  • Chengqun Li
  • Minzhi Wei
  • Yuanhua Lin
  • Efthymios G. Tsionas

Abstract

In this paper, we establish the existence of a solitary wave in a KdV-mKdV equation with dissipative perturbation by applying the geometric singular perturbation technique and Melnikov function. The distance of the stable manifold and unstable manifold is computed to show the existence of the homoclinic loop for the related ordinary differential equation systems on the slow manifold, which implies the existence of a solitary wave for the KdV-mKdV equation with dissipative perturbation.

Suggested Citation

  • Chengqun Li & Minzhi Wei & Yuanhua Lin & Efthymios G. Tsionas, 2021. "Existence of Solitary Waves in a Perturbed KdV-mKdV Equation," Journal of Mathematics, Hindawi, vol. 2021, pages 1-6, May.
    • Handle: RePEc:hin:jjmath:2270924
    DOI: 10.1155/2021/2270924
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