@Article{EAJAM-14-1,
author = {Yan, Xue-Wei and Yong, Chen and Tian, Shou-Fu and Xiu-Bin, Wang},
title = {Multi-Breather, Rogue Wave and Multi-Bright-Dark Soliton Interaction of the (2+1)-Dimensional Nonlocal Fokas System},
journal = {East Asian Journal on Applied Mathematics},
year = {2024},
volume = {14},
number = {1},
pages = {1--23},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2022-258.300123},
url = {https://global-sci.com/article/82396/multi-breather-rogue-wave-and-multi-bright-dark-soliton-interaction-of-the-21-dimensional-nonlocal-fokas-system}
}