Numerical spectral synthesis of breather gas for the focusing nonlinear Schr\"odinger equation

TL;DR

This paper numerically constructs and analyzes breather gases for the focusing nonlinear Schrödinger equation using high-precision simulations of ensembles of breathers, validating spectral kinetic theory predictions.

Contribution

It introduces a numerical method to realize breather gases with different spectral configurations and investigates their interaction properties.

Findings

Breather gases were successfully synthesized for three spectral types.

The propagation velocities of test breathers matched spectral kinetic theory predictions.

The study demonstrates the feasibility of numerical spectral synthesis for complex nonlinear wave ensembles.

Abstract

We numerically realize breather gas for the focusing nonlinear Schr\"odinger equation. This is done by building a random ensemble of N $\sim$ 50 breathers via the Darboux transform recursive scheme in high precision arithmetics. Three types of breather gases are synthesized according to the three prototypical spectral configurations corresponding the Akhmediev, Kuznetsov-Ma and Peregrine breathers as elementary quasi-particles of the respective gases. The interaction properties of the constructed breather gases are investigated by propagating through them a "trial" generic breather (Tajiri-Watanabe) and comparing the mean propagation velocity with the predictions of the recently developed spectral kinetic theory (El and Tovbis, PRE 2020).