Two-dimensional rogue waves on zero background in a Benney-Roskes model

Abstract

A prototypical example of a rogue wave (RW) structure in a two-dimensional (2D) nonlocal, nonlinear Schrödinger model, namely, a variant of the Benney-Roskes (BR) system, is presented. The analytical methodology involves a Taylor series expansion of an eigenfunction of the model's Lax pair, which is used to form a hierarchy of infinitely many eigenfunctions. These are used for the construction of 2D RWs of the BR system by the evenfold Darboux transformation. The obtained 2D RWs, which are localized in both space and time, can be viewed as a 2D analog of the Peregrine soliton.