Galilean-transformed solitons and supercontinuum generation in dispersive media

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 Schrödinger 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.

Subjects

Galilei transformation

Solitons

Supercontinuum generation

Nonlinear Sciences - Pattern Formation and Solitons

Physics - Fluid Dynamics

DDC Class

600: Technik

More Funding Information

J.M.D. acknowledges support from the French National Research Agency : ANR-15-IDEX-0003 , ANR-17-EURE-0002 , ANR-20-CE30-0004 , ANR-21-ESRE-0040 .

Lizenz

https://creativecommons.org/licenses/by/4.0/

Name

2201.05304v1.pdf

Type

Main Article

Size

3.93 MB

Format

Adobe PDF

Options

Galilean-transformed solitons and supercontinuum generation in dispersive media