Chirped nonlinear waves in the cubic-quintic distributed nonlinear Schrödinger equation with external trap, self-steepening and self-frequency shift

Abstract

A cubic-quintic inhomogeneous nonautonomous nonlinear Schrödinger (NLS) equation with an external trap, self-steepening, and self-frequency shift that models the transmission of nonlinear waves in nonautonomous inhomogeneous systems is considered. The integrability conditions under which the equation is converted into the standard NLS equation are obtained and a variety of nonlinear wave solutions with nonlinear chirping such as one-soliton solution, two-soliton solution, Akhmediev breather (AB) solution, Ma breather (MB) solution, as well as first- and second-order rogue wave (RW) solution are reported. We show how various parameters of either the model equation or the solutions may affect the nature of nonlinear waves with their frequency chirps propagating in nonautonomous inhomogeneous systems modeled by the NLS equation under consideration. The density profiles of nonlinear waves obtained from all these solutions are analyzed. These solutions are used for investigating analytically the dynamics of nonlinear waves in Bose-Einstein condensates (BECs) with both two- and three-body interatomic interactions when the gain/loss of atoms is taken into consideration. Considering BEC systems with time-independent trap frequency, we show that under a constant gain/loss parameter, the trap parameter can be used to convert triplet second-order RWs into either doublet second-order RWs or a composite of one bright solitary wave and a doublet second-order RWs. Also, our results reveal that for BECs with constant trap frequency under kink-like gain/loss parameter, the trap parameter can be used to convert (i) triplet second-order RWs into single second-order RWs, and (ii) two-soliton into doublet rogue wave. The family of chirped nonlinear wave solutions presented in this work may prove significance for designing the manipulation and transmission of nonlinear waves. Also, the found here results may provide possibilities to manipulate experimentally some nonlinear waves such as rogue waves or two-soliton in BEC systems.