Higher dimensional bright solitons and their collisions in a multicomponent long wave–short wave system

Abstract

Abstract. Bright plane soliton solutions of an integrable (2+1) dimensional (n + 1)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one long wave component are found and then the results are generalized to the corresponding integrable (n + 1)-wave system with n short waves and single long wave. It is shown that the solitons in the short wave components (say S(1) and S (2) ) can be amplified by merely reducing the pulse width of the long wave component (say L). The study on the collision dynamics reveals the interesting behaviour that the solitons which split up in the short wave components undergo shape changing collisions with intensity redistribution and amplitude-dependent phase shifts. Even though similar type of collision is possible in (1+1) dimensional multicomponent integrable systems, to our knowledge for the first time we report this kind of collisions in (2+1) dimensions. However, solitons which appear in the long wave component exhibit only elastic collision though they undergo amplitude-dependent phase shifts.

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions

“…[17] and the exponentially localized (dromion) and periodic solutions were obtained using the truncated Painlevé approach [17]. The present authors (TK and KS) and their collaborators have obtained a more general N -soliton solution of the multicomponent (2+1)D LSRI system and revealed the fascinating energy sharing collision of bright solitons in the multicomponent two-dimensional LSRI system [18]. Also, the exact mixed (bright-dark) soliton solutions of the multicomponent (2+1)D LSRI system have been obtained and their underlying collisions were discussed in detail [19].…”

Bright-Dark Mixed N -Soliton Solution of Two-Dimensional Multicomponent Maccari System

“…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,…”

Векторные Акустические Солитоны При Взаимодействии Длинных И Коротких Волн В Парамагнитном Кристалле

“…Была получена система трех билинейных уравнений и найдены ее решения в терминах определителей Вронского. Решения, выражающиеся через определители Грама, были выведены в статье [32].…”