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

Li Li,Fajun Yu

doi:10.1038/s41598-017-10205-4

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.

Highlights

Rogue waves(RWs) are called the monster waves or extreme waves in the ocean, which are catastrophic natural physical phenomena1–5
Similarity reduction for the three-component coupled GP equation. It is well-known that the coupled GP equation is often used to describe the interactions among the modes in nonlinear optics, components in Bose-Einstein condensates (BECs), etc
We consider the effect of time-dependent quadratic potential on the structure and dynamic of rogue waves

Summary

Introduction

Rogue waves(RWs) are called the monster waves or extreme waves in the ocean, which are catastrophic natural physical phenomena (thunderstorms, earthquakes and hurricanes). Some important applications are presented in nonlinear optics and water wave tanks. Some important applications are presented in nonlinear optics and water wave tanks7 It universality stimulates a great deal of attention devoted to searching for exact solutions of the generalized NLS models. The studies of rogue wave in single-component system have indicated that the rational solution of the NLS equation can be used to describe the phenomenon well . Searching for the rogue waves or rational solutions of NLS equation is an interesting work, which can describe new physical phenomena. Matveev and Salle consider some important applications on DT in solitons, and give rise to the transformation properties of the 1-dimensional NLS equation in ref

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