Dissipative periodic waves, solitons and breathers of the nonlinear Schrodinger equation with complex potentials

TL;DR

This paper derives exact localized and periodic solutions for a generalized nonlinear Schrödinger equation with complex potentials, demonstrating the existence of stable dissipative breathers and analyzing their stability.

Contribution

It introduces a method to find exact solutions for NLS equations with complex inhomogeneous potentials, including stable dissipative breathers.

Findings

Exact localized and periodic solutions are obtained.

Stable and unstable solutions are identified.

Numerical evidence of stable dissipative breathers in traps.

Abstract

Exact solutions for the generalized nonlinear Schr\"odinger (NLS) equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a wide class of localized and periodic modulations in the space of complex potentials and nonlinearity coefficients. Examples of stable and unstable solutions are given. We also demonstrated numerically the existence of stable dissipative breathers in the presence of an additional parabolic trap.