TY - JOUR

T1 - Rogue waves in multiphase solutions of the focusing NLS equation

AU - Bertola, Marco

AU - El, Gennady

AU - Tovbis, Alex

PY - 2016/10/1

Y1 - 2016/10/1

N2 - Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalized rogue wave notion then naturally enters as a large-amplitude localized coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite-band potentials of the fNLS equation that exhibit generalized rogue waves.

AB - Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalized rogue wave notion then naturally enters as a large-amplitude localized coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite-band potentials of the fNLS equation that exhibit generalized rogue waves.

U2 - 10.1098/rspa.2016.0340

DO - 10.1098/rspa.2016.0340

M3 - Article

SN - 0080-4630

VL - 472

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

M1 - 20160340

ER -