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<p>In this paper, we discuss the dynamics and shape alterations of traveling waves associated with the Euler equations (EE) in shallow water in two space dimensions. The models include single traveling wave with different shapes, stability of solitons with respect to initial conditions, and head-on collisions of two fission traveling waves, splitting into an arbitrary many after interaction. The models are shown to be low-order asymptotic approximations to EE.</p>

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On Multi-fission and Fusion Interactions of Traveling Waves for the Two-Dimensional Euler Equations

  • 期刊论文

  • 发表日期：

    2025年2月5日

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  • Julio Paez,
  • Zhijun Qiao,
  • Vesselin Vatchev

摘要

In this paper, we discuss the dynamics and shape alterations of traveling waves associated with the Euler equations (EE) in shallow water in two space dimensions. The models include single traveling wave with different shapes, stability of solitons with respect to initial conditions, and head-on collisions of two fission traveling waves, splitting into an arbitrary many after interaction. The models are shown to be low-order asymptotic approximations to EE.