Two-breather solutions for the class I infinitely extended nonlinear Schrödinger equation and their special cases

Abstract

We derive the two-breather solution of the class I infinitely extended nonlinear Schrödinger equation. We present a general form of this multi-parameter solution that includes infinitely many free parameters of the equation and free parameters of the two-breather components. Particular cases of this solution include rogue wave triplets, and special cases of 'breather-tosoliton' and 'rogue wave-to-soliton' transformations. The presence of many parameters in the solution allows one to describe wave propagation problems with higher accuracy than with the use of the basic NLSE.

Concurrent instabilities causing multiple rogue waves in infinite-dimensional dynamical systems

“…In the early days, investigations on MI have been limited to the linear stability analysis of constant amplitude waves [8,9,32]. It was later realised that a long-time evolution of MI can be modelled by the nonlinear Schrödinger equation (NLSE) [33,34]. While the analytical solution of NLSE, called the Akhmediev Breather (AB) that describes full growth-return cycle of MI, has existed for more than 30 years [35,22,36], most theoretical investigations, until recently, have been carried out using numerical approaches and finite spectrum approximations [37].…”