Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation

Abstract

We numerically realize breather gas for the focusing nonlinear Schrödinger 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).

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Cited by in corpus (6)

• Soliton gas in integrable dispersive hydrodynamics
• Generalized hydrodynamics of the KdV soliton gas
• Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation
• Recent developments in spectral theory of the focusing NLS soliton and breather gases: the thermodynamic limit of average densities, fluxes and certain meromorphic differentials; periodic gases
• NonlinearSchrodinger: Higher-Order Algorithms and Darboux Transformations for Nonlinear Schrödinger Equations
• The formation of a soliton gas condensate for the focusing Nonlinear Schrödinger equation