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We present a formal demonstration that light can simultaneously exhibit a superfluid behavior and spatial long-range order when propagating in a photonic crystal with self-focussing nonlinearity. In this way, light presents the distinguishing features of matter in a supersolid phase. We show that this supersolid phase provides the stability conditions for nonlinear Bloch waves and, at the same time, permits the existence of topological solitons or defects for the envelope of these waves. We use a condensed matter analysis instead of a standard nonlinear optics approach and provide numerical evidence of these theoretical findings.
We demonstrate dynamical topological phase transitions in evolving Su-Schrieffer-Heeger (SSH) lattices made of interacting soliton arrays, which are entirely driven by nonlinearity and thereby exemplify emergent nonlinear topological phenomena. The p
We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson equation which i
Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous e
We investigate numerically and experimentally the influence of coupling disorder on the self-trapping dynamics in nonlinear one-dimensional optical waveguide arrays. The existence of a lower and upper bound of the effective average propagation consta
We study - experimentally, theoretically, and numerically - nonlinear excitations in lattices of magnets with long-range interactions. We examine breather solutions, which are spatially localized and periodic in time, in a chain with algebraically-de