Phase-suppressed hydrodynamics of solitons on constant-background plane wave

TL;DR

This paper experimentally demonstrates the critical role of initial phase-shift profiles in the hydrodynamic evolution of solitons and breathers on constant-background waves, showing how phase control affects their stability and maximal amplification.

Contribution

It provides the first experimental validation of the importance of initial phase excitation in the propagation of solitons and breathers in hydrodynamic media, aligning with NLSE predictions.

Findings

Zero initial phase shift causes soliton disintegration.

Phase control delays maximal wave amplification.

Experimental results agree with NLSE simulations.

Abstract

Soliton and breather solutions of the nonlinear Schr\"odinger equation (NLSE) are known to model localized structures in nonlinear dispersive media such as on the water surface. One of the conditions for an accurate propagation of such exact solutions is the proper generation of the exact initial phase-shift profile in the carrier wave, as defined by the NLSE envelope at a specific time or location. Here, we show experimentally the significance of such initial exact phase excitation during the hydrodynamic propagation of localized envelope solitons and breathers, which modulate a plane wave of constant amplitude (finite background). Using the example of stationary black solitons in intermediate water depth and pulsating Peregrine breathers in deep-water, we show how these localized envelopes disintegrate while they evolve over a long propagation distance when the initial phase shift is zero. By setting the envelope phases to zero, the dark solitons will disintegrate into two gray-type solitons and dispersive elements. In the case of the doubly-localized Peregrine breather the maximal amplification is considerably retarded; however locally, the shape of the maximal focused wave measured together with the respective signature phase-shift are almost identical to the exact analytical Peregrine characterization at its maximal compression location. The experiments, conducted in two large-scaled shallow-water as well as deep-water wave facilities, are in very good agreement with NLSE simulations for all cases.