Galilean-transformed solitons and supercontinuum generation in dispersive media

TL;DR

This study demonstrates that Galilean transformations can be applied to wave groups in dispersive media, revealing new dynamics such as self-modulation and supercontinuum generation, with implications for nonlinear wave systems.

Contribution

It shows that Galilean-transformed solitons exhibit distinct behaviors in dispersive media, including soliton fission and supercontinuum generation, expanding the applicability of Galilean symmetry in nonlinear wave analysis.

Findings

Galilean-transformed solitons show deviations from pure dynamics.

Positive Galilean velocity induces self-modulation of solitons.

Supercontinuum generation occurs due to soliton fission in the studied system.

Abstract

The Galilean transformation is a universal operation connecting the coordinates of a dynamical system, which move relative to each other with a constant speed. In the context of exact solutions of the universal nonlinear Schr\"odinger equation (NLSE), inducing a Galilean velocity (GV) to the pulse involves a frequency shift to satisfy the symmetry of the wave equation. As such, the Galilean transformation has been deemed to be not applicable to wave groups in nonlinear dispersive media. In this paper, we demonstrate that in a wave tank generated Galilean transformed envelope and Peregrine solitons show clear variations from their respective pure dynamics on the water surface. The type of deviations depends on the sign of the GV and can be captured by the modified NLSE or the Euler equations. Moreover, we show that positive Galilean-translated envelope soliton pulses exhibit self-modulation. While designated GS and wave steepness values expedite multi-soliton dynamics, the strong focusing of such higher-order coherent waves inevitably lead to the generation of supercontinua as a result of soliton fission. We anticipate that kindred experimental and numerical studies might be implemented in other dispersive wave guides governed by nonlinearity.