Eigenvalue cutoff in the cubic-quintic nonlinear Schrödinger equation

Self-trapping of vortex crystals via competing nonlinearities

We investigate the existence of self-trapped nonlinear waves with multiple phase singularities. Working with the cubic-quintic nonlinear Schrödinger equation, we focus on configurations with an antivortex surrounded by a triangular arrangement of vortices within a hosting soliton. We find stationary patterns that can be interpreted as stable self-trapped vortex crystals, constituting the first example of a configuration of this sort with space-independent potentials. Their stability is linked to their norm, transitioning from unstable to stable as their size increases, with an intermediate region where the structure is marginally unstable, undergoing a remarkable and puzzling self-reconstruction during its evolution.

Dynamics of vortex-antivortex pairs and rarefaction pulses in liquid light

We present a numerical study of the cubic-quintic nonlinear Schrödinger equation in two transverse dimensions, relevant for the propagation of light in certain exotic media. A well-known feature of the model is the existence of flat-top bright solitons of fixed intensity, whose dynamics resembles the physics of a liquid. They support traveling wave solutions, consisting of rarefaction pulses and vortex-antivortex pairs. In this work, we demonstrate how the vortex-antivortex pairs can be generated in bright soliton collisions displaying destructive interference followed by a snake instability. We then discuss the collisional dynamics of the dark excitations for different initial conditions. We describe a number of distinct phenomena including vortex exchange modes, quasielastic flyby scattering, solitonlike crossing, fully inelastic collisions, and rarefaction pulse merging.

Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity

We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT-symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT-symmetric cases. Interactions and collisions between the conservative and PT-symmetric solitons are briefly investigated, as well.

Drag force in bimodal cubic-quintic nonlinear Schrödinger equation

We consider a system of two cubic-quintic nonlinear Schrödinger equations in two dimensions, coupled by repulsive cubic terms. We analyze situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and analyze their interaction. We find a realization of D'Alembert's paradox for small velocities and nontrivial drag forces for larger ones. We present numerical analysis including the search of static and traveling form-preserving solutions along with simulations of the dynamical evolution in some representative examples.

Coherent cavitation in the liquid of light

We study the cubic- (focusing-)quintic (defocusing) nonlinear Schrödinger equation in two transverse dimensions. We discuss a family of stationary traveling waves, including rarefaction pulses and vortex-antivortex pairs, in a background of critical amplitude. We show that these rarefaction pulses can be generated inside a flattop soliton when a smaller bright soliton collides with it. The fate of the evolution strongly depends on the relative phase of the solitons. Among several possibilities, we find that the dark pulse can reemerge as a bright soliton.

Wave train generation of solitons in systems with higher-order nonlinearities

Considering the higher-order nonlinearities in a material can significantly change its behavior. We suggest the extended nonlinear Schrödinger equation to describe the propagation of ultrashort optical pulses through a dispersive medium with higher-order nonlinearities. Soliton trains are generated through the modulational instability and we point out the influence of the septic nonlinearity in the modulational instability gain. Experimental values are used for the numerical simulations and the input plane wave leads to the development of pulse trains, depending upon the sign of the septic nonlinearity.