Interactions among the Rogue Waves and Solitons for a (2+1)-dimensional Maccari System in Fluid Mechanics and Nonlinear Optics

• Autores: Yu Zhao, Bo Tian, Cong-Cong Hu, Su-Su Chen, Shao-Hua Liu
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 4, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we investigate a (2+1)-dimensional Maccari system in fluid mechanics and nonlinear optics. With the aid of the bilinear method and Kadomtsev-Petviashvili hierarchy reduction, we construct the semi-rational solutions. Based on the semirational solutions, hybrid solutions which illustrate the interactions among the Nthorder rogue waves and (N + 1) solitons are obtained, where N is a positive integer.

    Due to the interactions, the rogue waves in those hybrid solutions behave localized in two-dimensional space and in time. Hybrid solutions consisting of the first-order rogue wave and two solitons, and hybrid solutions consisting of the second-order rogue waves and three solitons are shown. There are two types of the rogue waves: the line rogue waves and rogue waves. For the hybrid solutions consisting of the first-order rogue wave and two solitons, the asymptotic forms and amplitudes of the two solitons are given. Furthermore, we study the relations between the amplitudes of the two types of rogue waves and the soliton phase parameters graphically. For the hybrid solutions consisting of the second-order rogue waves and three solitons, three different types of the line rogue waves or rogue waves are derived upon the relations among the soliton phase parameters.

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