Bright-dark solitons and their collisions in mixedN-coupled nonlinear Schrödinger equations

Abstract

Mixed type (bright-dark) soliton solutions of the integrable N-coupled nonlinear Schrödinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients are obtained by using Hirota's bilinearization method. Generally, for the mixed N-CNLS equations the bright and dark solitons can be split up in (N − 1) ways. By analysing the collision dynamics of these coupled bright and dark solitons systematically we point out that for N > 2, if the bright solitons appear in at least two components, non-trivial effects like onset of intensity redistribution, amplitude dependent phase-shift and change in relative separation distance take place in the bright solitons during collision. However their counterparts, the dark solitons, undergo elastic collision but experience the same amplitude dependent phase-shift as that of bright solitons. Thus in the mixed CNLS system there co-exist shape changing collision of bright solitons and elastic collision of dark solitons with amplitude dependent phase-shift, thereby influencing each other mutually in an intricate way.

Novel energy sharing collisions of multicomponent solitons

“…This system (1) admits three types of soliton solutions namely bright-bright, bright-dark, and dark-dark. It was found that the bright solitons exhibit a special type of energy sharing collisions where as the dark solitons always undergo elastic collision [16,18]. The Gram determinant form of the bright N -soliton solution (for arbitrary N ) has been obtained by Kanna et al, [16].…”

“…The above system admits bright soliton solutions for the Manakov (focusing) case and it supports both bright and bright-dark soliton solutions for the mixed-ICNLS case [11][12][13][14][15][16][17][18]. Particularly, the bright multi-soliton solutions of the multicomponent generalization of Manakov system have been obtained by Kanna et al using the Hirota bilinearization method and a detailed investigation on the soliton collisions, such as energy sharing collision and elastic type interactions, have been explored [14][15][16][17].…”

“…These Manakov and mixed-ICNLS systems find important applications in optical communication and in artificial metamaterials. They have been intensively studied in literature [2,[8][9][10][11][12][13][14][15][16][17][18][19]. Also, the integrable multicomponent generalization of ICNLS system (1) can be written as…”

Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds

“…As such, these states have also undergone intense theoretical investigation; see e.g. [45][46][47][48][49][50][51][52][53][54][55] for a number of relevant studies. The prototypical onedimensional model where such states can be found to arise is the coupled GPE [28] of the form:…”

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

“…Another same analysis, if the variation of Γ j (t) exist, the amplitudes of three soliton pairs will change followingly. Here, in the same way, one can also discuss the dynamic behaviour of other forms of soltion pairs such as two dark-dark soltions [7,46] and two brightdark soltions [47] by the transformation in Section 2.…”