Exploring the Salerno Model for Rogue Wave Generation: A Linear Stability Analysis Beyond the DNLS and AL Limits

• Published in: International journal of theoretical physics Vol. 62; no. 8
• Main Authors: Gupta, Mishu, Gupta, Rama, Malhotra, Shivani
• Format: Journal Article
• Language: English
• Published: New York Springer US 29.07.2023
• Subjects: Elementary Particles; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Field Theory; Quantum Physics; Theoretical; Mathematical modelling of rogue waves; Salerno model; Linearisation; Stability; Perturbation; Phase portraits
• ISSN: 1572-9575; 1572-9575
• DOI: 10.1007/s10773-023-05419-4

This study presents a detailed analysis of the Salerno equation, which is a novel mathematical model for rogue wave generation. The model bridges the discrete nonlinear Schrödinger model and the integrable Ablowitz-Ladik model. The dispersion relation is calculated to understand the relationship between the wavenumber and system parameters, and the study examines very high values of nonlinearity parameters. It is found that unstable spirals exist in this regime, and their fluctuations are subject to more underlying modes. The Jacobian and monodromy matrix calculations reveal the existence of rogue waves, and it is observed that knowledge of how the free parameters may help to tune and control rogue wave generation. The study provides an inclusive and innovative solution for energy and finds application in the generation of oceanic waves, optical lattices, Bose-Einstein condensates, and photorefractive crystals. The results of the stabilitsis of rogue waves for the Salerno model, obtained using linearization techniques, the evaluation of perturbation equation, evaluation of fixed points of the monodromy matrix closest to the rogue wave initial condition, phase portraits of the linearized and perturbed equation, are discussed in detail. Overall, this study significantly contributes to the understanding of rogue waves in nonlinear systems and highlights the potential of the Salerno equation for practical applications, providing insights into their complex dynamics and control, which can be beneficial in designing experiments for practical applications.