Solitary wave solutions of ac-driven nonlinear Schrödinger equation supported by localized gain-loss

Abstract

In this study, we investigate solitary wave solutions of the ac-driven nonlinear Schrödinger equation supported by localized gain-loss. By modifying the model equation to incorporate nonlinear loss, we derive exact analytical solutions for both localized and wave-train patterns. Utilizing powerful mathematical tools such as Möbius and fractional transformations, we identify analytical bright, dark, and periodic solutions, outlining the entire phase plot of the model parameters where these solutions are possible under both trivial and non-trivial chirping conditions. Our results demonstrate the model's versatility, providing a robust framework for the design and control of optical systems. This work advances the theoretical framework for dissipative solitons with significant potential for real-world applications in high-capacity telecommunications and optical frequency combs.