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<p>The interaction of a solitary wave with an external force is studied within the framework of a modified Korteweg-de Vries equation, accounting for viscosity and damping. Using asymptotic methods, a dynamical system is derived to describe the amplitude and phase of the solitary wave. A bifurcation analysis of this system is presented, depending on the parameters characterizing viscosity and flow, and the conditions for the trapping of the solitary wave by the external force are examined. The obtained asymptotic results are compared with direct numerical simulations. The asymptotic and numerical results agree for all types of equilibrium points in the dynamical system.</p>

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Soliton dynamics under the influence of an external force and induced-damped terms within the modified Korteweg-de Vries equation

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Ioann Melnikov,
  • Marcelo V. Flamarion

摘要

The interaction of a solitary wave with an external force is studied within the framework of a modified Korteweg-de Vries equation, accounting for viscosity and damping. Using asymptotic methods, a dynamical system is derived to describe the amplitude and phase of the solitary wave. A bifurcation analysis of this system is presented, depending on the parameters characterizing viscosity and flow, and the conditions for the trapping of the solitary wave by the external force are examined. The obtained asymptotic results are compared with direct numerical simulations. The asymptotic and numerical results agree for all types of equilibrium points in the dynamical system.