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<p>This paper investigates an extended (2+1)-dimensional modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff (mKdV-CBS) equation. The integrability properties of the equation are given, including the bilinear form, the Bäcklund transformation, and the Lax pair. The multi-soliton solutions are constructed via the Hirota bilinear method. By virtue of the long-wave limit technique, the second- and third-order positon solutions are derived, and the interaction solutions of <i>n</i> second-order positons are further obtained accordingly. The expression for the interaction solution between <i>n</i>-soliton and second-order positon is presented for the first time. More general and asymmetric asymptotic trajectories are proposed, with distinct forms applicable to multi-positon solutions and positon-soliton interaction solutions, respectively. Furthermore, the detailed analysis of elastic interaction phenomena is provided, such as soliton-positon, breather-positon, and soliton-breather. This study significantly enriches the known solution structure of this integrable system and provides deep insights into complex nonlinear wave dynamics in higher-dimensional space.</p>

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Dynamics of soliton, positon and interaction solutions to the extended (2+1)-dimensional mKdV-CBS equation

  • 期刊论文

  • 发表日期：

    2026年2月14日

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  • Si-Jia Chen,
  • Xing Lü

摘要

This paper investigates an extended (2+1)-dimensional modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff (mKdV-CBS) equation. The integrability properties of the equation are given, including the bilinear form, the Bäcklund transformation, and the Lax pair. The multi-soliton solutions are constructed via the Hirota bilinear method. By virtue of the long-wave limit technique, the second- and third-order positon solutions are derived, and the interaction solutions of n second-order positons are further obtained accordingly. The expression for the interaction solution between n-soliton and second-order positon is presented for the first time. More general and asymmetric asymptotic trajectories are proposed, with distinct forms applicable to multi-positon solutions and positon-soliton interaction solutions, respectively. Furthermore, the detailed analysis of elastic interaction phenomena is provided, such as soliton-positon, breather-positon, and soliton-breather. This study significantly enriches the known solution structure of this integrable system and provides deep insights into complex nonlinear wave dynamics in higher-dimensional space.