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We study numerically the statistics of waves for generalized one-dimensional Nonlinear Schrodinger (NLS) equation that takes into account focusing six-wave interactions, dumping and pumping terms. We demonstrate the universal behavior of this system for the region of parameters when six-wave interactions term affects significantly only the largest waves. In particular, in the statistically steady state of this system the probability density function (PDF) of wave amplitudes turns out to be strongly non-Rayleigh one for large waves, with characteristic fat tail decaying with amplitude $|Psi|$ close to $proptoexp(-gamma|Psi|)$, where $gamma>0$ is constant. The corresponding non-Rayleigh addition to the PDF indicates strong intermittency, vanishes in the absence of six-wave interactions, and increases with six-wave coupling coefficient.
Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrodinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of
We investigate 1D and 2D radial domain-wall (DW) states in the system of two nonlinear-Schr{o}dinger/Gross-Pitaevskii equations, which are coupled by the linear mixing and by the nonlinear XPM (cross-phase-modulation). The system has straightforward
We report results of the analysis of the spontaneous symmetry breaking (SSB) in the basic (actually, simplest) model which is capable to produce the SSB phenomenology in the one-dimensional setting. It is based on the Gross-Pitaevskii - nonlinear Sch
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying soliton states.
We investigate competition between two phase transitions of the second kind induced by the self-attractive nonlinearity, viz., self-trapping of the leaky modes, and spontaneous symmetry breaking (SSB) of both fully trapped and leaky states. We use a