Beak-shaped rogue waves for a higher-order coupled nonlinear Schrodinger system with 4 x 4 Lax pair

In this paper, we investigate the beak-shaped rogue waves for a higher-order coupled nonlinear Schrodinger system. Firstly, we construct a 4 x 4 Lax pair and the Nth-order Darboux transformation. Secondly, with the non-zero seed solutions, we derive the Nth-order beak-shaped rogue wave solutions and beak-shaped rogue wave pair solutions. Then, via such solutions, we graphically illustrate the nature of the beak-shaped rogue waves and beak-shaped rogue wave pairs. Moreover, we find that the width and angle of the beak-shaped rogue wave along the space axis enlarge with the increase of a real parameter in the higher-order coupled nonlinear Schrodinger system. We present two distinct types of the second-order vector beak-shaped rogue waves: one with the triangle pattern and the other one with the merged pattern. We show the first-order vector beak-shaped rogue wave pair and two distinct types of the second-order vector beak-shaped rogue wave pairs with the triangle pattern and merged pattern. (c) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates beak-shaped rogue waves in a higher-order coupled nonlinear Schrodinger system, obtaining corresponding solutions through the construction of Lax pairs and Darboux transformations, and observes changes in the characteristics of beak-shaped rogue waves along the space axis with increasing real parameters.