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arXiv · 2101.05547

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

Giacomo Roberti·Gennady El·Alexander Tovbis·François Copie·Pierre Suret·Stéphane Randoux
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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).

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Giacomo Roberti, Gennady El, Alexander Tovbis, François Copie, Pierre Suret, Stéphane Randoux. 2021-01-14. Numerical spectral synthesis of breather gas for the focusing nonlinear Schr\"odinger equation. https://doi.org/10.1103/physreve.103.042205

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