Anisotropic Coupled Nonlinear Schrödinger–Ginzburg–Landau System with Dissipation and Cross-Phase Modulation

Abstract

In this paper, we introduce a novel analytical model, the Anisotropic Coupled Nonlinear Schrödinger-Ginzburg-Landau (A-CNLS-GL) system, incorporating dissipation, cross-phase modulation, and anisotropic effects. Such a model is pivotal for studying the formation and dynamics of stable, self-organized structures like dissipative solitons and light bullets in complex physical systems, including nonlinear optical media and Bose-Einstein condensates. We employ the powerful Modified Extended Tanh-Function Method to derive many exact analytical solutions, including dark, bright, singular, and periodic soliton solutions. Furthermore, we explore additional solutions using exponential and hyperbolic ansatzes. The discussion covers the physical interpretation of the solutions. The behaviour of the solutions is illustrated through graphs, showing how energy evolves and how the coupled fields maintain balance. The model and method prove to be robust and versatile, suggesting strong potential for use in photonics and quantum fluid dynamics.