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Employing a particularly suitable higher order symplectic integration algorithm, we integrate the 1-$d$ nonlinear Schr\"odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering off an…
A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the…
We present a series of experimental investigations on binary mixtures of Bose-Einstein condensates. Our focus lies on the regime where the interaction parameters place the system at the threshold of miscibility. We demonstrate that the…
We study (2+1)-dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents, and demonstrate that these solitary waves exhibit a symmetry-breaking instability provided their total…
The nonlinear dispersive wave equation inside the cylindrical elastic rod is derived by applying the Navier-Bernoulli hypothesis and Love's relation in \cite{5}. The elastic rod is assumed to be composed of the Murnaghan's materials such as…
We discuss the dynamics of interacting dark-bright two-dimensional vector solitons in multicomponent immiscible bulk Bose-Einstein condensates. We describe matter-wave molecules without a scalar counterpart that can be seen as bound states…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
We have investigated mixed-gap vector solitons involving incoherently coupled fundamental and dipole components in a parity-time (PT) symmetric lattice with saturable nonlinearity. For the focusing case, vector solitons emerge from the…
We report results of systematic investigation of dynamics featured by moving two-dimensional (2D) solitons generated by the fractional nonlinear Schroedinger equation (FNLSE) with the cubic-quintic nonlinearity. The motion of solitons is a…
We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The…
We have investigated the nonlinear amplitude vector equation governing the evolution of optical pulses in optical and UV region. We are normalizing this equation for the cases of different and equal transverse and longitudinal size of…
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…
We present a stability analysis of a modified nonlinear Schroedinger equation describing the propagation of ultra-short pulses in negative refractive index media. Moreover, using methods of quantum statistics, we derive a kinetic equation…
We study the dynamics of a dark-bright soliton interacting with a fixed impurity using a mean-field approach. The system is described by a vector nonlinear Schrodinger equation (NLSE) appropriate to multicomponent Bose-Einstein condensates.…
We overview the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by a sequence of linear and nonlinear layers. First, we consider a single layer with a cubic nonlinear response…
The results of recent experiments [1] on observing soliton lattices and their dislocations in vertical cylindrical channels filled with immiscible fluids with strongly different viscosities and but slightly different densities are…
We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended…
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with low-dimensional (1D) conservative plus dissipative nonlinear optical lattices are investigated. In the case of focusing media (with attractive…
We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…
In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schr\"odinger equations, which is a nonintegrable system…