Non-autonomous multi-rogue waves for spin-1 coupled nonlinear Gross-Pitaevskii equation and management by external potentials

Abstract

We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows us to relate certain class of multi-rogue wave solutions of the spin-1 coupled nonlinear GP equation to the solutions of integrable coupled nonlinear Schrödinger(CNLS) equation. We study the effect of time-dependent quadratic potential on the profile and dynamic of non-autonomous rogue waves. With certain requirement on the backgrounds, some non-autonomous multi-rogue wave solutions exhibit the different shapes with two peaks and dip in bright-dark rogue waves. Then, the managements with external potential and dynamic behaviors of these solutions are investigated analytically. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers and super-fluids.

Provable bounds for the Korteweg–de Vries reduction in multi-component nonlinear Schrödinger equation

“…Nonetheless, we will keep our main motivation as non-equilibrium dynamics in Bose mixtures [2]. In the context of cold atoms, vector nonlinear Schrödinger equation (VNLS) (aka multi-component Gross-Pitaevskii equation) appears in multiple coupled species of bosons [35][36][37][38][39][40][41][42][43][44][45][46] or bosons with hyperfine degrees of freedom (spinor BECs [47][48][49][50][51][52][53][54][55]). The nonlinearities or interactions one sees are of inter-species and intra-species type.…”

Low relativistic effects on the modulational instability of rogue waves in electronegative plasmas

“…For instance, it has been well established that they may appear in physical systems as the consequence of the interplay between nonlinear and dispersive effects, under the activation of the so-called MI phenomenon [3][4][5][6][7][8]. Recently, interest in studying RWs has gone beyond oceanography and hydrodynamics [9,10] to reach some other areas related to optics and photonics [11][12][13][14], Bose-Einstein condensation [15][16][17], biophysics [18][19][20][21], plasma physics [22,23], just to name a few. Particularly, ion-acoustic super-RWs were found in an ultra-cold neutral plasma in the presence of ion-fluid and nonextensive electron distribution [24].…”

Discrete Bright-dark Soliton Interaction Dynamic Behaviors for Nonautonomous 2+1-Dimensional Soliton Equation

“…And, a discrete rogue-wave solution of Ablowitz-Musslimani equation with parity-time symmetric potential is derived in [21]. The non-autonomous rogue wave, bright, dark and breather solutions of nonlinear Gross-Pitaevskii(GP) equation are investigated in [22,23]. Several non-autonomous dark-bright solutions of the generalized three-coupled GP equations are obtained in [24].…”