We introduce novel classes of higher-order spatial optical solitons in analogy with Laguerre-Gaussian and Hermite-Gaussian linear eigenmodes. We reveal that stable higher-order optical solitons can exist in nonlocal nonlinear media in the various forms of soliton necklaces and soliton matrices. Modulational instability can lead to nontrivial transformations between energetically close solitons ...

We study pattern formation that is due to modulational instability of noncollinear counterpropagating beams. Angular misalignment of the pumps over a broad range leads to the generation of lines oriented perpendicular to the plane of the pump beams. A theoretical expression for the angular separation of the lines is in close agreement with observations. Outside this range, for both small and la...

Propagation of a modulationally amplified Gaussian pulse is considered inside a birefringent optical fiber. We show analytically that, in addition to a reduction in the parametric gain and a change in the pulse’s group velocity, the third-order dispersion allows the generation of a temporal Airy-shaped pulse. Furthermore, pulse spreading in the temporal domain and chirping in the spectral domai...

We report frequency conversion experiments in silicon-on-insulator (SOI) directional couplers. We demonstrate that the evanescent coupling between two subwavelength SOI waveguides is strongly dispersive and significantly modifies modulational instability (MI) spectra through the coupling induced group velocity dispersion (GVD). As the separation between two 380-nm-wide silicon photonic wires de...

We demonstrate that a dielectric medium with purely quadratic nonlinearity [the so-called chi((2)) material] can display self-focusing phenomena through a new type of modulational instability of the interacting fundamental and second-harmonic field components and therefore can support propagation of (two-wave) optical solitons. We prove the existence of a family of such solitons, which are foun...

We numerically investigate the conical emission (CE) from ultrashort laser filaments, both considering and disregarding the higher-order Kerr effect (HOKE). While the consideration of HOKE has almost no influence on the predicted CE from collimated beams, differences arise for tightly focused beams. This difference is attributed to the different relative contributions of the nonlinear focus and...

We present a method to construct a symplecticity preserving renormalization group map of a chain of weakly nonlinear symplectic maps and obtain a general reduced symplectic map describing its long-time behaviour. It is found that the modulational instability in the reduced map triggers random wandering of orbits around some homoclinic-like manifolds, which is understood as the Bernoulli shifts....

The trigger for the nonlinear destabilization of the double tearing mode (DTM), referred to as a structuredriven instability leading to explosive growth and subsequent collapse, is investigated. We use the reduced MHD equations that solve the evolution of perturbations from an equilibrium deformed by two-dimensional magnetic islands during the slow evolution of the quasi-steady nonlinear regime...

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is ...

For a dissipative variant of the two-dimensional Gross-Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas-Fermi radius. The instability occurs as a result of a linear instability of a vortex-free stea...