Rogue waves on the background of periodic standing waves in the derivative NLS equation

TL;DR

This paper investigates rogue waves on periodic backgrounds in the derivative NLS equation, revealing conditions for their localization and providing analytical and numerical results on their amplitudes.

Contribution

It introduces exact rogue wave solutions on periodic standing waves in the DNLS equation and analyzes their localization conditions based on modulational stability.

Findings

Rogue waves are localized only on modulationally unstable backgrounds.

Stable backgrounds lead to algebraic solitons instead of rogue waves.

Maximal rogue wave amplitudes are derived analytically and confirmed numerically.

Abstract

The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the DNLS equation. We show that the space-time localization of a rogue wave is only possible if the periodic standing wave is modulationally unstable. If the periodic standing wave is modulationally stable, the rogue wave solutions degenerate into algebraic solitons propagating along the background and interacting with the periodic standing waves. Maximal amplitudes of rogue waves are found analytically and confirmed numerically.