Research Article
Dynamics of Generalized Unstable Nonlinear Schrödinger Equation: Instabilities, Solitons, and Rogue Waves
Issue:
Volume 11, Issue 1, March 2025
Pages:
1-18
Received:
30 October 2024
Accepted:
10 December 2024
Published:
20 January 2025
DOI:
10.11648/j.ijamtp.20251101.11
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Abstract: This study delves into the dynamics of the unstable Schrödinger equation, employing three distinct analytical methods: the complex envelope function ansatz, the generalized Tanh method, and the Bernoulli sub-ODE method. By leveraging the complex envelope function technique, we uncover solutions for various optical soliton types, including dark optical solitons, bright optical solitons, and bright-dark optical solitons. Notably, this method facilitates an in-depth examination of individual soliton intensity profiles, providing valuable insights into their behavior. Furthermore, we utilize the generalized Tanh method and the Bernoulli sub-ODE method to derive solutions involving hyperbolic and trigonometric functions. These solutions shed light on the intricate dynamics of nonlinear optical phenomena within the framework of the Schrödinger equation. The obtained solutions are graphically illustrated, showcasing dark, bright, dark-bright, and singular solitons. Our research contributes significantly to the understanding of unstable Schrödinger equation dynamics, offering a comprehensive analysis of optical soliton behavior. The conservation laws of the model equation are also constructed, providing a deeper understanding of the underlying physical principles. This study’s findings have important implications for the development of advanced optical communication systems and the study of nonlinear optical phenomen.
Abstract: This study delves into the dynamics of the unstable Schrödinger equation, employing three distinct analytical methods: the complex envelope function ansatz, the generalized Tanh method, and the Bernoulli sub-ODE method. By leveraging the complex envelope function technique, we uncover solutions for various optical soliton types, including dark opti...
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