Mixed solitons in a (2+1)-dimensional multicomponent long-wave–short-wave system

Abstract

We derive a (2+1)-dimensional multicomponent long-wave-short-wave resonance interaction (LSRI) system as the evolution equation for propagation of N-dispersive waves in weak Kerr-type nonlinear medium in the small-amplitude limit. The mixed- (bright-dark) type soliton solutions of a particular (2+1)-dimensional multicomponent LSRI system, deduced from the general multicomponent higher-dimensional LSRI system, are obtained by applying the Hirota's bilinearization method. Particularly, we show that the solitons in the LSRI system with two short-wave components behave like scalar solitons. We point out that for an N-component LSRI system with N>3, if the bright solitons appear in at least two components, interesting collision behavior takes place, resulting in energy exchange among the bright solitons. However, the dark solitons undergo standard elastic collision accompanied by a position shift and a phase shift. Our analysis on the mixed bound solitons shows that the additional degree of freedom which arises due to the higher-dimensional nature of the system results in a wide range of parameters for which the soliton collision can take place.

Bright-Dark MixedN-Soliton Solution of Two-Dimensional Multicomponent Maccari System

“…Hence, different from the 2-b-1-d case, the two solitons in all the components (short-wave and long-wave components) for the 1-b-2-d case always undertake standard elastic collision without energy exchange. It is worth noting that this phenomenon is consistent with the mixed soliton solution of the three-component YO system [13,16]. The mixed-type two solitons are displayed in Fig.??…”

“…Based on the above tau functions, the asymptotic analysis of the two-soliton solution can be performed as in Refs. [11,13], this will help us to elucidate the understanding of the collision of two solitons. Particularly, we study the interaction of two solitons in the x-y plane.…”

“…Of particular interest is the multi-component generalization of the nonlinear Schrödinger (NLS) equation [5][6][7][8][9][10], which has been considered as the generic model to describe the evolution of slowly varying wave packets in nonlinear wave systems. What's more, the study on nonlinear systems describing the interaction of long waves with short wave packets in nonlinear dispersive media has received much attentions in recent years [11][12][13][14][15][16]. Such systems have found wide applications in the fields of hydrodynamics, nonlinear optics, plasma physics and so on [17][18][19][20].…”

“…For instance, in Bose-Einstein condensates [21], the nonlinear coefficients take positive or negative when the interaction between the atoms is repulsive or attractive. For some multi-component systems [11,13,16], it has been found that the solitons exhibit certain energy-exchanging inelastic collision behaviors, which have not been found in the single-component counterparts and may be used to realize multi-state logic and soliton collision-based computing. In the current paper, we consider the multi-component generalization of the Mel'nikov system [23][24][25][26] iΦ y = Φ xx + uΦ,…”

GeneralN-Dark Soliton Solutions of the Multi-Component Mel’nikov System

“…Of particular interest is the multi-component generalization of the nonlinear Schrödinger (NLS) equation, the so-called vector NLS equation [8][9][10][11][12][13]. Another interesting example is the multi-component long-wave-short-wave resonance interaction (LSRI) system [14][15][16], or the so called multi-component Yajima-Oikawa (YO) system [17][18][19][20].…”