Abstract A coupled (2+ 1)-dimensional variable coefficient Ginzburg–Landau equation is
studied. By virtue of the modified Hirota bilinear method, the bright one-soliton solution of the …

We investigate the non-isospectral generalized higher order NLS equation (GHNLS) with
external potential which is unswervingly represents the ultrashort optical soliton …

A variable-coefficients nonisospectral nonlinear Schrödinger (vc-nNLS) equation is
investigated. Integrable background in the framework of the Lax pair with a time-dependent …

Soliton molecules are firstly obtained by velocity resonance for the Gerdjikov–Ivanov
equation, and n-order smooth positon solutions for the Gerdjikov–Ivanov equation are …

In this work, the existence of nonlinear ring waves in the form of multi-solitons is investigated
analytically by considering a non-isospectral Nonlinear Schrödinger (NLS) equation with …

Solutions of the classical and nonlocal Gross–Pitaevskii (GP) equation with a parabolic
potential and a gain term are derived by using a second-order nonisospectral Ablowitz …

We investigate the nonisospectral effects of a semi-discrete nonlinear Schrödinger equation,
which is a direct integrable discretization of its continuous counterpart. Bilinear form and …

We begin by introducing a non-isospectral Lax pair, from which we derive a non-isospectral
integrable Kaup–Newell hierarchy. The new general solutions for the non-isospectral …

In this paper an integrable Gross–Pitaevskii equation with a parabolic potential and a gain
term is investigated. Its solutions with a nonzero background are derived. These solutions …

Abstract The (2+ 1)-dimensional nonlocal breaking solitons AKNS hierarchy and the
nonlocal negative order AKNS hierarchy are presented. Solutions in double Wronskian form …