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<p>Rogue waves on the background of periodic standing waves in the (3+1)-dimensional nonlinear evolution equation are presented by the nonlinearization of the Lax pair and multi-fold Darboux transformation. The (3+1)-dimensional nonlinear evolution equation is decomposed into a Schrödinger equation and two (1+1)-dimensional soliton equations. By combining the nonlinearization of the Lax pair and Darboux transformation, two types rogue wave solutions to the (3+1)-dimensional nonlinear evolution equation on the background of the Jacobian elliptic functions dn and cn are derived. In addition, the evolution process of the equation is demonstrated through numerical simulation. This paper enriches the rogue wave solutions of multi-dimensional equations on the periodic background.</p>

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Rogue periodic waves in the (3+1)-dimensional nonlinear evolution equation

  • 期刊论文

  • 发表日期：

    2025年6月5日

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  • Wurile,
  • Gong Maoguo,
  • Zhaqilao

摘要

Rogue waves on the background of periodic standing waves in the (3+1)-dimensional nonlinear evolution equation are presented by the nonlinearization of the Lax pair and multi-fold Darboux transformation. The (3+1)-dimensional nonlinear evolution equation is decomposed into a Schrödinger equation and two (1+1)-dimensional soliton equations. By combining the nonlinearization of the Lax pair and Darboux transformation, two types rogue wave solutions to the (3+1)-dimensional nonlinear evolution equation on the background of the Jacobian elliptic functions dn and cn are derived. In addition, the evolution process of the equation is demonstrated through numerical simulation. This paper enriches the rogue wave solutions of multi-dimensional equations on the periodic background.