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We consider the problem of the formation of soliton states from a modulationally unstable initial condition in the framework of the Schrodinger-Poisson (or Newton-Schrodinger) equation accounting for gravitational interactions. We unveil a previously unrecognized regime: By increasing the nonlinearity, the system self-organizes into an incoherent localized structure that contains hidden coherent soliton states. The solitons are hidden in the sense that they are fully immersed in random wave fluctuations: The radius of the soliton is much larger than the correlation radius of the incoherent fluctuations while its peak amplitude is of the same order of such fluctuations. Accordingly, the solitons can hardly be identified in the usual spatial or spectral domains, while their existence is clearly unveiled in the phase-space representation. Our multi-scale theory based on coupled coherent-incoherent wave turbulence formalisms reveals that the hidden solitons are stabilized and trapped by the incoherent localized structure. Furthermore, hidden binary soliton systems are identified numerically and described theoretically. The regime of hidden solitons is of potential interest for self-gravitating Boson models of fuzzy dark matter. It also sheds new light on the quantum-to-classical correspondence with gravitational interactions. The hidden solitons can be observed in nonlocal nonlinear optics experiments through the measurement of the spatial spectrogram.
The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in the framew
The generation of high-intensity optical fields from harmonic-wave photons, interacting via a cross-phase modulation with dark solitons both propagating in a Kerr nonlinear medium, is examined. The focus is on a pump consisting of time-entangled dark
We investigate the interaction between a light beam and a two-dimensional photonic lattice that is photo-induced in a photorefractive crystal using partially coherent light. We demonstrate that this interaction process is associated with a host of ne
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condense
We report the numerical realization and demonstration of robustness of certain 2-component structures in Bose-Einstein Condensates in 2 and 3 spatial dimensions with non-trivial topological charge in one of the components. In particular, we identify