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<p>In this paper, we consider a nonlinear equation modeling the free surface evolution of moderate amplitude waves in shallow water containing backward diffusion and dissipation. By means of the geometric singular perturbation and invariant manifold theory, we show that this equation admits solitary wave solutions.</p>

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Existence of Solitary Wave Solutions for the Perturbed Shallow Water Wave Equation of Moderate Amplitude

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月3日

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  • Jing Yan,
  • Bo Jiang

摘要

In this paper, we consider a nonlinear equation modeling the free surface evolution of moderate amplitude waves in shallow water containing backward diffusion and dissipation. By means of the geometric singular perturbation and invariant manifold theory, we show that this equation admits solitary wave solutions.