We report the prediction of fully localized two-dimensional embedded solitons. These solitons are obtained in a quasi-one-dimensional waveguide array which is periodic along one spatial direction and localized along the orthogonal direction. Under appropriate nonlinearity, these solitons are found to exist inside the Bloch bands (continuous spectrum) of the waveguide and thus are embedded solit...

We show that, for the 1d cubic NLS equation, widely separated equal amplitude in-phase solitons attract and opposite-phase solitons repel. Our result gives an exact description of the evolution of the two solitons valid until the solitons have moved a distance comparable to the logarithm of the initial separation. Our method does not use the inverse scattering theory and should be applicable to...

It is shown that self-guided optical beams with power-law asymptotics, i.e., algebraic optical solitons, can be regarded as a special case of sech-type solitons ~i.e. solitons with exponentially decaying asymptotics! in the limit where the beam propagation constant coincides with the threshold for linear wave propagation. This leads to the conjecture that algebraic optical solitons should be in...

We analyze dark solitons supported by second-order parametric interactions between the fundamental and second harmonics in the presence of dispersion and group-velocity mismatch. We reveal various types of solitary waves, including a family of two-wave dark solitons propagating on a modulationally stable background, dark solitons with nonmonotonic tails, and bound states of dark solitons.

Symmetry breaking is reported for continuous families of solitons in the nonlinear Schrödinger equation with a two-dimensional complex potential. This symmetry breaking is forbidden in generic complex potentials. However, for a special class of partially parity-time-symmetric potentials, it is allowed. At the bifurcation point, two branches of asymmetric solitons bifurcate out from the base bra...

We report results of a systematic study of one-dimensional four-wave moving solitons in a recently proposed model of the Bragg cross-grating in planar optical waveguides with the Kerr nonlinearity; the same model applies to a fiber Bragg grating (BG) carrying two polarizations of light. We concentrate on the case when the system’s spectrum contains no true bandgap, but only semi-gaps (which are...

We present a detailed overview of the physics and applications of optical dark solitons: localized nonlinear waves (or ‘holes’) existing on a stable continuous wave (or extended finite-width) background. Together with the traditional problems involving properties of dark solitons of the defocusing cubic nonlinear Schrödinger equation, we also describe recent theoretical results on optical vorte...

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in n...

We study composite spatial optical solitons supported by two-wave mutual focusing induced by cross-phase modulation in Kerr-like nonlinear media. We find the families of both singleand two-hump solitons and discuss their properties and stability. We also reveal remarkable similarities between recently predicted holographic solitons in photorefractive media and parametric solitons in quadratic n...

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic Non-Linear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the cla...