Dynamics of rational and semi-rational solutions of the general N-component nonlinear Schrödinger equations
Year: 2024
Type: article
Abstract: We investigate an integrable general N -component nonlinear Schrödinger equations. The Darboux-dressing transformation for the equations is firstly constructed according to its Lax pair. Applying the idea of separating variables, we generate the solutions of the Lax pair equations with a nontrivial background. Then we derive the rational and semi-rational vector solutions of the equations in detail. The rational solutions act as the pure rogue waves. The semi-rational solutions represent a combination of different types of rogue waves, breathers, and soliton waves. Moreover, a constraint condition is given for the semi-rational solutions being reduced to unmixed breather or n th-rogue waves. To illustrate the corresponding dynamic behaviors of these solutions, we analyze two-component and four-component cases, showing that the multi-component system exhibits richer phenomena and novel behaviors compared to lower-component systems, and also presenting some novel phenomena.
Source: Applied Mathematical Modelling
Author: Wei-Qi Peng
Institution: Ocean University of China
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,980
OpenAlex ID: W4402905065