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<p>Nonlinear Schrödinger equation and derivative nonlinear Schrödinger equation play the pivotal roles in nonlinear optics. In this paper, we mainly investigate a high-order modified derivative nonlinear Schrödinger (h-MDNLS) equation through Darboux transformation method, which can be obtained from the generalized modified derivative nonlinear Schrödinger (g-MDNLS) hierarchy with constraints. A variety of analytic solutions are constructed. We present exact soliton solutions of the h-MDNLS equation based on the zero seed solution. Furthermore, we analyze the dynamics and asymptotic behavior of the two-soliton solutions. Interestingly, the breather wave is generated by the interaction of two parallel solitary waves. In addition, we also derive the breather solutions, including Kuznetsov–Ma (KM) breather, Akhmediev breather and rational solutions of the h-MDNLS equation with the nonzero seed solution. We must emphasize that breather solutions and rational solutions of the h-MDNLS equation are studied for the first time, which have not been reported in the literature.</p>

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Soliton, breather and rational solutions of a high-order modified derivative nonlinear Schrödinger equation

  • 期刊论文

  • 发表日期：

    2025年4月5日

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  • Hong-Qian Sun,
  • Jun-Hua Huang,
  • Li-Yuan Ma

摘要

Nonlinear Schrödinger equation and derivative nonlinear Schrödinger equation play the pivotal roles in nonlinear optics. In this paper, we mainly investigate a high-order modified derivative nonlinear Schrödinger (h-MDNLS) equation through Darboux transformation method, which can be obtained from the generalized modified derivative nonlinear Schrödinger (g-MDNLS) hierarchy with constraints. A variety of analytic solutions are constructed. We present exact soliton solutions of the h-MDNLS equation based on the zero seed solution. Furthermore, we analyze the dynamics and asymptotic behavior of the two-soliton solutions. Interestingly, the breather wave is generated by the interaction of two parallel solitary waves. In addition, we also derive the breather solutions, including Kuznetsov–Ma (KM) breather, Akhmediev breather and rational solutions of the h-MDNLS equation with the nonzero seed solution. We must emphasize that breather solutions and rational solutions of the h-MDNLS equation are studied for the first time, which have not been reported in the literature.