Rogue wave formation and interactions in the defocusing nonlinear Schr\"odinger equation with external potentials

TL;DR

This paper discovers novel rogue waves and W-shaped solitons in the defocusing nonlinear Schrödinger equation with external potentials, revealing new wave phenomena previously thought absent in such systems.

Contribution

It introduces the existence of stable rogue waves and W-shaped solitons in the defocusing NLS equation with various external potentials, a phenomenon not observed before.

Findings

Stable rogue waves found in defocusing NLS with real-valued potentials

Higher amplitude rogue waves generated through interactions

Rogue waves and solitons also appear in PT-symmetric complex potentials

Abstract

The defocusing nonlinear Schr\"odinger (NLS) equation has no the modulational instability, and was not found to possess the rogue wave (RW) phenomenon up to now. In this paper, we firstly investigate some novel nonlinear wave structures in the defocusing NLS equation with real-valued time-dependent and time-independent potentials such that the stable new RWs and W-shaped solitons are found, respectively. Moreover, the interactions of two or three RWs are explored such that the RWs with higher amplitudes are generated in the defocusing NLS equation with real-valued time-dependent potentials. Finally, we study the defocusing NLS equation with complex PT -symmetric potentials such that some RWs and W-shaped solitons are also found. These novel results will be useful to design the related physical experiments to generate the RW phenomena and W-shaped solitons in the case of defocusing nonlinear interactions, and to apply them in the related fields of nonlinear or even linear sciences.