Multisoliton solutions of the two-component Camassa-Holm equation and their reductions (Mathematical Aspects and Applications of Nonlinear Wave Phenomena)

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  • Matsuno, Yoshimasa
    Division of Applied Mathematical Science, Graduate School of Sciences and Technology for Innovation, Yamaguchi University

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Other Title
  • 2成分Camassa-Holm方程式の多重ソリトン解とその簡約 (非線形波動現象の数理とその応用)
  • 2成分Camassa-Holm方程式の多重ソリトン解とその簡約
  • 2 セイブン Camassa-Holm ホウテイシキ ノ タジュウ ソリトンカイ ト ソノ カンヤク

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Abstract

The two-component Camassa-Holm (CH2) equation models the propagation of nonlinear surface gravity waves on shallow water. It has several remarkable features. Among them, it is a completely integrable system. By employing a direct method in soliton theory, we develop a systematic procedure for constructing multisoliton solutions of the CH2 equation, and explore their properties. Then, we show that the two integrable reductions are possible for the CH2 equation by means of appropriate scaling limits, leading to the CH and two component Hunter-Saxton equations. The reduced form of multisoliton solutions is presented for both equations.

Journal

  • RIMS Kokyuroku

    RIMS Kokyuroku 2034 166-179, 2017-07

    京都大学数理解析研究所

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