Multi-breather asymptotics for a nonlinear Schrödinger equation arising in oceanography, plasma physics, Bose–Einstein condensation and fiber optics

Nonlinear Schrödinger (NLS)-type equations describe various physics phenomena in the nonlinear media in oceanography, plasma physics, Bose–Einstein condensation and fiber optics. This paper deals with the $N$-breather solutions in the determinant form for a cubic-focusing NLS equation, claimed to be the most fundamental form among the NLS-type quations, where $N$ is a positive integer. We carry out an asymptotic analysis on the $N$-breather solutions and obtain the algebraic expressions for the individual breather components. The physical characteristics of the $N$ interacting breathers, including their characteristic lines, phase shifts, energy exchanges, periods, and extreme points, are discussed. Before and after the interactions, the $N$ breather components pass through each other without any change in shape or velocity, while their solitary and periodic parts encounter the phase shifts. Taking the 3D plot and density plot of the two interacting breathers as an example, our asymptotic results are consistent with those plots. Our work may enhance the understanding of the multi-breather interactions in various physics contexts, and the method used can be extended to other NLS-type equations across the diverse physical phenomena.