Multi-dark soliton solutions for the (2+1)-dimensional multi-component Maccari system

Abstract

Based on the KP hierarchy reduction method, the general multi-dark soliton solutions in Gram type determinant forms for the multi-component coupled Maccari system are constructed. Especially, the three-component coupled Maccari system comprised of two-component short waves and single-component long waves are discussed in detail. Besides, the dynamics of one and two darkdark solitons are analyzed. It is shown that the collisions of two dark-dark solitons are elastic by asymptotic analysis. Additionally, the two dark-dark solitons bound states are studied through two different cases (stationary and moving cases). The bound states can exist up to arbitrary order in the stationary case, however, only two-soliton bound state exists in the moving case. Besides, the oblique stationary bound state can be generated for all possible combinations of nonlinearity coefficients consisted of positive, negative and mixed cases. Nevertheless, the parallel stationary and the moving bound states are only possible when nonlinearity coefficients take opposite signs.

A class of nonlinear wave patterns for (2+1) dimensional coupled integrable Maccari’s system

“…The propagation of soliton solution for various systems such as the modified inhomogeneous Hirota equation [20], inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system [21], Schrödinger Maxwell-Bloch equation [22] and Hirota-MB equation [23] are studied through the Darboux transformation method. The Exp-function approach [24], the generalized Riccati relation [25], the extended Fan sub-equation method [26], the bilinear method [27], reduction of the KP hierarchy [28], and closed-form solutions with arbitrary parameters have all been effectively found.…”

Doubly localized two‐dimensional rogue waves generated by resonant collision in Maccari system

“…[30][31][32][33][34][35][36][37][38][39] Moreover, the RW solution in the two-dimensional analogue, Davey-Stewartson (DS) equation, has also been widely studied. 18,[40][41][42] Thus, as a relatively new two-dimensional extension of the NLS equation, the Maccari system 43,44 is an interesting model to looking for doubly localized two-dimensional RWs and the generating mechanism from view of wave interaction. This is the main purpose of this paper.…”

Collisional Dynamics of Dromion Triplet for (2+1) Dimensional Coupled Integrable Maccari’s System

“…In recent years, notable advancements have been identified in the study of MS to generate solutions in the closed form. The Exp-function approach [45], the generalised Riccati relation [46], the extended Fan sub-equation method [47], the bilinear method [48], the extended modified auxiliary equation mapping method [49], and closed-form solutions with arbitrary parameters have all been effectively found.…”