Solitons are ubiquitous and exist in almost every area from sky to bottom. For solitons to appear, the relevant equation of motion must be nonlinear. In the present study, we deal with the Korteweg-deVries (KdV), Modied Korteweg-de Vries (mKdV) and Regularised LongWave (RLW) equations using Homotopy Perturbation method (HPM). The algorithm makes use of the HPM to determine the initial expansion...

We use the variational method to find the optimum launch conditions that can sustain path-averaged solitons in a periodically amplified, constant-dispersion, optical communication system even when amplifier spacing is comparable to or larger than the dispersion length. We determine the amount of prechirping and the initial peak power required and show that both the pulse width and the chirp rec...

Stability of solitons in parity-time (PT )-symmetric periodic potentials (optical lattices) is analyzed in both oneand two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice rises above a certain threshold (phase transition point), an infinite number of linear Bloch bands turn complex simultaneously. Second, we show that while sta...

Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of "gap-acoustic" solitons (GASs), for which we find exact analytic solutions. The GAS consists of an optical pulse similar to the optical gap soliton, dressed by an accompanying phonon pulse. Close to t...

We report systematic results of collisions between discrete spatiotemporal optical solitons in twodimensional photonic lattices. We show that the outcomes of collisions strongly depend on the initial soliton parameters, such as their input amplitudes (energies) and their transverse velocities. Four generic outcomes are identified in the study of collisions between discrete light bullets located...

Microcavity polaritons are composite half-light half-matter quasiparticles, which have recently been demonstrated to exhibit rich physical properties, such as nonequilibrium condensation, parametric scattering and superfluidity. At the same time, polaritons have important advantages over photons for information processing, since their excitonic component leads to weaker diffraction and stronger...

We discuss the properties of composite (or vector) spatial optical solitons created by the incoherent interaction of two optical beams and associated with higher-order modes guided by a soliton-induced waveguide in a bulk medium. Such stationary (2 1 1)-dimensional self-trapped localized structures include, in particular, vortexand dipole-mode vector solitons and also incorporate higher-order m...

For three decades optical spatial solitons confined in the transverse plane were commonly believed to be a prerogative of media with cubiclike nonlinearities @1#. A remarkable exception is the work carried out in Ref. @2#, where the possibility to achieve diffraction-free propagation via threephoton interactions in quadratic media ~henceforth, parametric solitons! was first pointed out. The fie...

Solitons are localized nonlinear waves and occur in many branches of physics. Their properties have provided a deep and fundamental understanding of complex nonlinear systems. In recent years, there has been considerable interest in studying solitons in systems with periodic potentials or lattices, in particular, those that can be generated in nonlinear optical materials [1]–[5]. In periodic la...

We demonstrate self-trapping of light by simultaneously compensating normal and anomalous (saddle-shaped) diffractions with self-focusing and self-defocusing hybrid nonlinearity in optically induced ionic-type photonic lattices. Innovative two-dimensional gap solitons, named "saddle solitons," are established, whose phase and spectrum characteristics are different from all previously observed s...