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Solitons, the distinct balance between nonlinearity and dispersion, provide a route toward ultrafast electromagnetic pulse shaping, high-harmonic generation, real-time image processing, and RF photonic communications. Here we newly explore…
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying…
The degrees of freedom inherent in spatiotemporal optical vortices (STOV's) afford intriguing opportunties to manipulate complex light fields for broad applications such as optical communication, light-matter interactions, particle…
We demonstrate the possibility of stopping the soliton pulses in optical waveguide with varying and constant parameters exhibiting a Kerr nonlinear response. By using the similarity transformation, we have found the constraint condition for…
The phenomenon of dynamical localization of matter wave solitons in optical lattices is first demonstrated and the conditions for its existence are discussed. In addition to the trapping linear periodic potential we use a periodic…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
Stable two- and three-dimensional spatiotemporal solitons (STSs) in second-harmonic-generating media are found in the case of normal dispersion at the second harmonic (SH). This result, surprising from the theoretical viewpoint, opens a way…
In this paper, we propose a second-order dynamical system with a smoothing effect for solving paramonotone variational inequalities. Under standard assumptions, we prove that the trajectories of this dynamical system converges to a solution…
Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were…
We present a formal demonstration that light can simultaneously exhibit a superfluid behavior and spatial long-range order when propagating in a photonic crystal with self-focussing nonlinearity. In this way, light presents the…
Soliton interactions in systems modelled by coupled nonlinear Schroedinger (CNLS) equations and encountered in phenomena such as wave propagation in optical fibers and photorefractive media possess unusual features : shape changing…
A conceptually new notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers…
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…
We predict random-phase spatial solitons in instantaneous nonlocal nonlinear media. The key mechanism responsible for self-trapping of such incoherent wave-packets is played by the non-local (rather than the traditional non-instantaneous)…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
Using the numerical solution of the nonlinear Schroedinger equation and a variational method it is shown that (3+1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr…
Soliton microcombs -- phase-locked microcavity frequency combs -- have become the foundation of several classical technologies in integrated photonics, including spectroscopy, LiDAR, and optical computing. Despite the predicted multimode…
We analyze nonlinear collective effects near surfaces of semi-infinite periodic systems with multi-gap transmission spectra and introduce a novel concept of multi-gap surface solitons as mutually trapped surface states with the components…
Using an example of a Raman active medium we describe how a common nonlinear process of four-wave mixing can be used to induce strong coupling between the spatial and temporal degrees of freedom in optical waves. This coupling produces…
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…