Pattern Formation and Solitons
Existence and stability of PT-symmetric gap solitons in a periodic structure with defocusing nonlocal nonlinearity are studied both theoretically and numerically. We find that, for any degree of nonlocality, gap solitons are always unstable…
Weakly-nonlinear waves in a layered waveguide with an imperfect interface (soft bonding between the layers) can be modelled using coupled Boussinesq equations. We assume that the materials of the layers have close mechanical properties, in…
Our aim in the present work is to identify all the possible standing wave configurations involving few vortices of different charges in an atomic Bose-Einstein condensate (BEC). In this effort, we deploy the use of a computational algebra…
Exceptional dicretizations of the phi4 model are reviewed, corresponding conservation laws are reported, and the properties of static and moving discrete kinks are discussed. Different approaches to producing such discretizations are given…
We analyze a coupled bulk-membrane PDE model in which a scalar linear 2-D bulk diffusion process is coupled through a linear Robin boundary condition to a two-component 1-D reaction-diffusion (RD) system with Gierer-Meinhardt (nonlinear)…
Interactions between solitons and the coherent oscillation structures generated by localized disturbances via modulational instability are studied within the framework of the focusing nonlinear Schrodinger equation. Two main interaction…
We study the stability and bifurcation structure of spatially extended patterns arising in nonlin- ear optical resonators with a Kerr-type nonlinearity and anomalous group velocity dispersion, as described by the Lugiato-Lefever equation.…
We study numerically the properties of (statistically) homogeneous soliton gas depending on soliton density (proportional to number of solitons per unit length) and soliton velocities, in the framework of the focusing one-dimensional…
We present results on stripe formation in the Swift-Hohenberg equation with a directional quenching term. Stripes are "grown" in the wake of a moving parameter step line, and we analyze how the orientation of stripes changes depending on…
The formation and development of oscillations is an important traffic flow phenomenon. Recent studies found that along a vehicle platoon described in the Lagrangian specification, traffic oscillations grow in a concave way. Since stationary…
We study experimentally, in a large-scale basin, the propagation of unidirectional deep water gravity waves stochastically modulated in phase. We observe the emergence of nonlinear localized structures that evolve on a stochastic wave…
The combination of linear and nonlinear potentials, both shaped as a single well, enables competition between the confinement and expulsion induced by the former and latter potentials, respectively. We demonstrate that this setting leads to…
We study dynamics of Dirac solitons in prototypical networks modeling them by the nonlinear Dirac equation on metric graphs. Soliton solutions of the nonlinear Dirac equation on simple metric graphs are obtained. It is shown that these…
The effects of nonlocal and reflecting connectivities have been previously investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange of electrical signals between neurons. In this work we investigate the…
We study the selftrapping properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder. In the weak nonlinearity regime, the dynamics is controlled by the degeneracy of the…
In this paper we review the physical relevance of a Korteweg-de Vries (KdV) equation with higher-order dispersion terms which is used in the applied sciences and engineering. We also present exact traveling wave solutions to this…
In the present work, motivated by numerous recent experimental developments we revisit the dynamics of a single vortex ring in anisotropic harmonic traps. At the theoretical level, we start from a general Lagrangian dynamically capturing…
We derive stationary solutions to the two-dimensional hyperbolic discrete nonlinear Schr\"odinger (HDNLS) equation by starting from the anti-continuum limit and extending solutions to include nearest-neighbor interactions in the coupling…
One dimensional lattice with an on-site cubic-quintic nonlinear response described by a cubic-quintic discrete nonlinear Schr\"odinger equation is tested for asymmetric wave propagation. The lattice is connected to linear side chains.…
We address the generation and interaction of dispersion-managed dissipative solitons (DMDS) in a model of fiber lasers with the cubic-quintic nonlinearity, multiphoton absorption and gain dispersion. Both anomalous and normal segments of…