Related papers: Vector nematicons
We study focussing discrete nonlinear Schr\"{o}dinger equations and present a new variational existence proof for homoclinic standing waves (bright solitons). Our approach relies on the constrained maximization of an energy functional and…
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities and numerically find…
In uniaxial soft matter with a reorientational nonlinearity, such as nematic liquid crystals, a light beam in the extraordinary polarization walks off its wavevector due to birefringence, while it undergoes self-focusing via an increase in…
We investigate the localized waves of the coupled two-mode nonlinear Schr\"{o}dinger equations with a pair-tunneling term representing strongly interacting particles can tunnel between the modes as a fragmented pair. Facilitated by Darboux…
We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave…
We consider the coupled propagation of an optical field and its second harmonic in a quadratic nonlinear medium governed by a coupled system of Schrodinger equations. We prove the existence of ring-profiled optical vortex solitons appearing…
We analyse the structure of the exact, dark and bright soliton solutions of the driven non-linear Schr\"odinger equation. It is found that, a wide class of solutions of the higher order non-linear Schr\"odinger equation with a source can…
There has been found an exact solution of the mixed problem for Shrodinger's compact U(m)-vector nonlinear model with an arbitrary sign of the coupling constant. It is shown, that in case of m>2 there is a new class of solutions - mixed…
Two discretizations of the vector nonlinear Schrodinger (NLS) equation are studied. One of these discretizations, referred to as the symmetric system, is a natural vector extension of the scalar integrable discrete NLS equation. The other…
We introduce a general model which augments the one-dimensional nonlinear Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a…
We address the interactions between optical solitons in the system with longitudinally varying nonlocality degree and nonlinearity strength. We consider a physical model describing light propagation in nematic liquid crystals featuring a…
Two-dimensional (2D) vector matter waves in the form of soliton-vortex and vortex-vortex pairs are investigated for the case of attractive intracomponent interaction in two-component Bose-Einstein condensates. Both attractive and repulsive…
Dynamics of solitons is considered in the framework of an extended nonlinear Schr\"odinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped…
Although most soliton research has traditionally considered dominant quadratic dispersion, the recent discovery of pure-quartic solitons has inspired analysis of soliton solutions with large higher orders of dispersion. Here we present…
Multi-component Bose-Einstein condensates exhibit an intriguing variety of nonlinear structures. In recent theoretical work, the notion of magnetic solitons has been introduced. Here we generalize this concept to vector dark-antidark…
New two-component soliton solutions of the coupled high-frequency (HF) - low-frequency (LF) system, based on Schr\"odinger - Korteweg - de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the…
We elucidate the properties of mixed-gap vector surface solitons supported by the interface between a uniform medium and an optical lattice imprinted in a Kerr-type nonlinear media. The components of such mixed-gap solitons emerge from…
We study dark solitons near potential and nonlinearity steps and combinations thereof, forming rectangular barriers. This setting is relevant to the contexts of atomic Bose-Einstein condensates (where such steps can be realized by using…
We investigate bright solitons in the one-dimensional Schr\"odinger equation in the framework of an extended variational approach. We apply the latter to the stationary ground state of the system as well as to coherent collisions between…
The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation with a periodic potential is demonstrated by means of the variational approximation (VA)…