Abstract

The concept of soliton gas (SG) as a large ensemble of solitons randomly distributed on an infinite line and elastically has been first introduced by Zakharov [Sov. Phys. JETP 33 , 538 (1971)]. Zakharov’s kinetic equation describes diluted SG and has been generalized to the case of a dense SG [Phys. Rev. Lett. 95,204101 (2005), PRE , 101, 052207 (2020)]. The SG is characterized by a density of state (DOS) which corresponds to the spatial distribution of the spectral parameters (in the framework of inverse scattering transform.   We report the generation and the measurement of SG in water waves and in optical fiber experiments [Phys Rev. Lett. 125, 264101 (2020)]. We show that the asymptotic stage of the noise-induced modulation instability corresponds to a SG having a specific DOS . This SG can be described by a N-soliton solution of the focusing one-dimensional nonlinear Schrödinger equation (1DNLSE). Our investigations reveal a remarkable agreement between spectral (Fourier) and statistical properties of the long-term evolution of the MI (observed in experiments and in numerical simulations of the 1DNLSE) and those of a constructed multisoliton, random-phase bound states [Phys. Rev. Lett. 123 (23), 234102 (2019)].