Solitons in Kerr media are the most well-studied solitons in nature. The reason for that is twofold. First, the Kerr nonlinearity can be found in many systems: It represents a weak symmetric anharmonicity, which is equivalent to a weak saturation in a simple harmonic oscillator. For electromagnetic waves propagating in a weakly nonlinear centrosymmetric dielectric media, the Kerr nonlinearity m...

We derive two systems of coupled-mode equations for spatial gap solitons in one-dimensional (1D) and quasi-one-dimensional (Q1D) photonic lattices induced by two interfering optical beams in a nonlinear photorefractive crystal. The models differ from the ordinary coupled-mode system (e.g., for the fiber Bragg grating) by saturable nonlinearity and, if expanded to cubic terms, by the presence of...

We study solitons in scalar theories with polynomial interactions on the fuzzy sphere. Such solitons are described by projection operators of rank k, and hence the moduli space for the solitons is the Grassmannian Gr(k, 2j+1). The gradient term of the action provides a non-trivial potential on Gr(k, 2j+1), thus reducing the moduli space. We construct configurations corresponding to wellseparate...

In recent years, there has seen much interest and increased research activities in Ricci solitons. Ricci solitons are natural generalizations of Einstein metrics. They are also special solutions to Hamilton’s Ricci flow and play important roles in the singularity study of the Ricci flow. In this paper, we survey some of the recent progress on Ricci solitons. The concept of Ricci solitons was in...

We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. T...

An optical time division multiplexing (TDM) scheme using soliton interaction is proposed in the thesis to save the time-bandwidth prduct (TBP). The soliton multiplexer (MUX) consisting of a highly nonlinear fiber (HNLF) combines two adjacent solitons to form a composite soliton, while the soliton demultiplexer (DEMUX) consisting of a similar HNLF restores the component solitons. The case of int...

We explore recently predicted multifrequency 2p solitons in multicascade stimulated Raman scattering (SRS) that was mode locked by the dynamics of population at a Raman quantum transition; we show that these solitons are eigensolitons of a general solitary-wave solution. Soliton components at each frequency are bright pulses of the same (Lorentzian) shape, in contrast to the familiar bright–dar...

We report on the spin properties of bright polariton solitons supported by an external pump to compensate losses. We observe robust circularly polarized solitons when a circularly polarized pump is applied, a result attributed to phase synchronization between nondegenerate TE and TM polarized polariton modes at high momenta. For the case of a linearly polarized pump, either σ+ or σ- circularly ...

We provide a detailed description of solutions of Curve Shortening in Rn that are invariant under some one-parameter symmetry group of the equation, paying particular attention to geometric properties of the curves, and the asymptotic properties of their ends. We find generalized helices, and a connection with curve shortening on the unit sphere Sn−1. Expanding rotating solitons turn out to be ...

We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localized waves, namely, parametric vortex solitons due to phase-matched second-harmonic generation in an optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic ...