Peregrine Solitons on a Periodic Background in the Vector Cubic-Quintic Nonlinear Schrödinger Equation

Yanlin Ye,Dumitru Mihalache,Shihua Chen,Fabio Baronio,Lili Bu,Wanwan Wang

doi:10.3389/fphy.2020.596950

Abstract

We present exact explicit Peregrine soliton solutions based on a periodic-wave background caused by the interference in the vector cubic-quintic nonlinear Schrodinger equation involving the self-steepening effect. It is shown that such periodic Peregrine soliton solutions can be expressed as a linear superposition of two fundamental Peregrine solitons of different continuous-wave backgrounds. Because of the self-steepening effect, some interesting Peregrine soliton dynamics such as ultrastrong amplitude enhancement and rogue wave coexistence are still present when they are built on a periodic background. We numerically confirm the stability of these analytical solutions against non-integrable perturbations, i.e., when the coefficient relation that enables the integrability of the vector model is slightly lifted. We also demonstrate the interaction of two Peregrine solitons on the same periodic background under some specific parameter conditions. We expect that these results may shed more light on our understanding of the realistic rogue wave behaviors occurring in either the fiber-optic telecommunication links or the crossing seas.

Highlights

Rogue waves refer to the surface gravity waves occurring in the open ocean whose wave heights are at least twice as high as the significant wave height of the surrounding waves [1]
We present exact explicit Peregrine soliton solutions based on a periodic-wave background caused by the interference in the vector cubic-quintic nonlinear Schrödinger equation involving the self-steepening effect
We presented exact Peregrine soliton solutions built on a periodic background caused by the interference in the vector CQ-nonlinear Schrödinger (NLS) equation involving self-steepening

Summary

INTRODUCTION

Rogue waves refer to the surface gravity waves occurring in the open ocean whose wave heights are at least twice as high as the significant wave height of the surrounding waves [1]. A typical example is the Peregrine soliton, which is a fundamental rational solution of the celebrated NLS equation [24] This type of soliton solution exhibits a single doubly-localized peak on a finite background, with its peak position and constant phase all undetermined, matching well the fleeting and transient wave characteristics of rogue waves as witnessed in real world. We present explicitly the general Peregrine soliton solutions built on such a periodic background, which were not reported previously, to the best of our knowledge The robustness of these analytical solutions against non-integrable perturbations has been numerically confirmed, by lifting the integrality condition of the above vector CQ-NLS model. The underlying mechanisms responsible for the generation of such periodic Peregrine solitons are discussed

THEORETICAL FRAMEWORK

INTRIGUING ROGUE WAVE DYNAMICS ON A PERIODIC BACKGROUND

CONCLUSIONS

DATA AVAILABILITY STATEMENT