Multi-Breather, Rogue Wave and Multi-Bright-Dark Soliton Interaction of the (2+1)-Dimensional Nonlocal Fokas System

Multi-Breather, Rogue Wave and Multi-Bright-Dark Soliton Interaction of the (2+1)-Dimensional Nonlocal Fokas System

Year:    2024

Author:    Xue-Wei Yan, Yong Chen, Shou-Fu Tian, Xiu-Bin Wang

East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 1 : pp. 1–23

Abstract

We study the (2+1)-dimensional nonlocal Fokas system by using the Hirota’s bilinear method. Firstly, a general tau-function of Kadomtsev-Petviashvili (KP) hierarchy satisfied with the bilinear equation under nonzero boundary condition is derived by considering differential relations and a variable transformation. Secondly, two Gram-type solutions are utilized to the construction of multi-breather, high-order rogue wave, and multi-bright-dark soliton solutions. Then the corresponding parameter restrictions of these solutions are given to satisfy with the complex conjugation symmetry. Furthermore, we find that if the parameter $p_{iI}$ takes different values, the rogue wave solution can be classified as three types of states, such as dark-dark, four-peak and bright-bright high-order rogue wave. If the parameter $c_i$ takes different values, the soliton solution can be classified as three type of states, including the multi-dark, multi-bright-dark and multi-bright solitons. By considering third-type of reduced tau-function to the Hirota’s bilinear equations, we give the collisions between the high-order rogue wave and the multi-bright-dark solitons on constant ($N$ is positive even) or periodic background ($N$ is positive odd). In order to understand the dynamics behaviors of the obtained solutions better, the various rich patterns are theoretically and graphically analyzed in detail.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.2022-258.300123

East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 1 : pp. 1–23

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    (2+1)-dimensional nonlocal Fokas system KP hierarchy reduction multi-breather wave high-order rogue wave multi-bright-dark soliton.

Author Details

Xue-Wei Yan

Yong Chen

Shou-Fu Tian

Xiu-Bin Wang