Rao Jiguang, Porsezian Kuppuswamy, He Jingsong, Kanna Thambithurai
Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China.
Department of Physics, Pondicherry University, Puducherry 605014, India.
Proc Math Phys Eng Sci. 2018 Jan;474(2209):20170627. doi: 10.1098/rspa.2017.0627. Epub 2018 Jan 17.
General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave-short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe (≥2) lumps annihilating into or producing from -dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.
通过采用双线性方法，得到了一个包含多个短波和一个长波的可积多分量(2 + 1)维长波-短波共振相互作用系统的一般半有理解。这些解描述了各种类型解之间的相互作用，包括线怪波、团块、呼吸子和暗孤子。在本文中，我们只关注团块和暗孤子之间相互作用的动力学行为。我们的详细研究揭示了两种不同类型的激发现象：融合和裂变。结果表明，基本（最简单）的半有理解可以表现出暗孤子裂变为一个团块和一个暗孤子，或者一个团块和一个暗孤子融合为一个暗孤子。非基本半有理解进一步分为三个子类：高阶、多类型和混合型半有理解。高阶半有理解展示了两个或更多团块湮灭（产生）为一个暗孤子（从一个暗孤子产生）的过程。多半有理解描述了（≥2）个团块湮灭为暗孤子或从暗孤子产生的情况。混合型半有理解是高阶半有理解和多半有理解的混合。对于混合型半有理解，我们展示了一种有趣的动力学行为，其特征是暗孤子对团块的部分抑制或产生。
