Scholarlink

<p>The Kuralay-II equation is an important integrable model, which is a typical form of the famous Heisenberg ferromagnet equation. Here, we study the Kuralay-II equation via the generalized perturbation (<i>n</i>,&#xa0;<i>N</i>-<i>n</i>)-fold Darboux transformation (gDT). By choosing suitable plane-wave seed solutions, we obtain various novel localized vector wave solutions, which contain high-order vector Akhmediev breathers, vector Kuznetsov–Ma breathers, vector rogue waves as well as their interactions. To inspect dynamical behaviors such vector wave solutions may possess, we present some illustrative numerical simulations, which show that the modulating control parameters selected have great impacts on the categories of the solutions and their structures as well as propagation properties. The results obtained are new and useful for experts to understand the corresponding phenomena in fluids, nonlinear optics and related fields. The gDT method introduced can be effectively used to construct localized waves to other nonlinear integrable systems.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Novel localized vector wave solutions in the Kuralay-II equation

  • 期刊论文

  • 发表日期：

    2025年7月7日

查看全文
  • Hongli An,
  • Zheng Liu,
  • Manwai Yuen

摘要

The Kuralay-II equation is an important integrable model, which is a typical form of the famous Heisenberg ferromagnet equation. Here, we study the Kuralay-II equation via the generalized perturbation (n, N-n)-fold Darboux transformation (gDT). By choosing suitable plane-wave seed solutions, we obtain various novel localized vector wave solutions, which contain high-order vector Akhmediev breathers, vector Kuznetsov–Ma breathers, vector rogue waves as well as their interactions. To inspect dynamical behaviors such vector wave solutions may possess, we present some illustrative numerical simulations, which show that the modulating control parameters selected have great impacts on the categories of the solutions and their structures as well as propagation properties. The results obtained are new and useful for experts to understand the corresponding phenomena in fluids, nonlinear optics and related fields. The gDT method introduced can be effectively used to construct localized waves to other nonlinear integrable systems.