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<p>In this paper, we study two two-component integrable generalizations of the Camassa–Holm equation with cubic nonlinear terms appeared in the classification work done by Hone et al. (Nonlinearity 30:622–658, 2017). For both systems, which are referred to as the 2gCH-I and 2gCH-II equations respectively, we construct their Bäcklund transformations and the corresponding nonlinear superposition formulas. As applications, some novel solutions to these two equations are calculated. For the 2gCH-I equation, interesting solutions include the fission and fusion of kinks as well as the kink–kink collisions. As for the 2gCH-II equation, the solutions obtained are smooth soliton solutions, singular soliton solutions and their various interactions.</p>

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Kinks fission and fusion, solitons and their interactions for two two-component generalizations of the Camassa–Holm equation with cubic nonlinearity: Bäcklund transformation approach

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Xing-Lan Li,
  • Q. P. Liu

摘要

In this paper, we study two two-component integrable generalizations of the Camassa–Holm equation with cubic nonlinear terms appeared in the classification work done by Hone et al. (Nonlinearity 30:622–658, 2017). For both systems, which are referred to as the 2gCH-I and 2gCH-II equations respectively, we construct their Bäcklund transformations and the corresponding nonlinear superposition formulas. As applications, some novel solutions to these two equations are calculated. For the 2gCH-I equation, interesting solutions include the fission and fusion of kinks as well as the kink–kink collisions. As for the 2gCH-II equation, the solutions obtained are smooth soliton solutions, singular soliton solutions and their various interactions.