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<p>In this paper, the high-order cubic-quintic nonlinear Schrödinger equation is considered. By overcoming the difficulties caused by its non-integrability, we completely explore the existence, uniqueness and stability of the limit cycle of the equation. It enables us to accurately give the explicit parameter representation of its periodic wave solution in a special form for the first time. These results provide not only a new idea of obtaining periodic solutions in complex nonlinear systems, but also the important theoretical support for understanding related wave phenomena.</p>

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Existence, Uniqueness, Stability and Exact Expression of Periodic Traveling Wave Solutions of the Higher-Order Cubic-Quintic Nonlinear Schrödinger Equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月29日

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  • Nan Wang,
  • Yuqian Zhou,
  • Zhijun Qiao

摘要

In this paper, the high-order cubic-quintic nonlinear Schrödinger equation is considered. By overcoming the difficulties caused by its non-integrability, we completely explore the existence, uniqueness and stability of the limit cycle of the equation. It enables us to accurately give the explicit parameter representation of its periodic wave solution in a special form for the first time. These results provide not only a new idea of obtaining periodic solutions in complex nonlinear systems, but also the important theoretical support for understanding related wave phenomena.