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We study numerically a parametrically driven discrete nonlinear Schr\"odinger equation modelling periodically curved waveguide arrays. We show that discrete surface solitons persist, but their threshold power is altered by the drive. There…
We study the classical dynamics of a system comprising a pair of Kerr-Duffing nonlinear oscillators, which are coupled through a nonlinear interaction and subjected to a parametric drive. Using the rotating wave approximation (RWA), we…
Phase control of parametric modulation in coupled oscillator networks enables sculpting of dynamical states with desired spatiotemporal symmetries. Symmetry-aware Floquet analysis successfully predicts such states in linear systems, but…
In this paper, we study how to apply a periodic driving field to control stable spin tunneling in a non-Hermitian spin-orbit coupled bosonic double-well system. By means of a high-frequency approximation, we obtain the analytical Floquet…
We present an analytical framework for stabilizing second-order correlated tunneling of two spin-orbit-coupled bosons in a periodically driven non-Hermitian double-well potential. By combining Floquet theory with multiple-scale asymptotic…
We study the nonequilibrium dynamics of two particles confined in two spatially separated harmonic potentials and linearly coupled to the same thermally fluctuating scalar field, a cartoon for optically trapped colloids in contact with a…
We study the driven tunneling of a one-dimensional charged particle confined to a rectangular double-well. The numerical simulation of the Schr\"odinger equation based on the Cranck-Nicholson finite-difference scheme, shows that the…
We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schr\"odinger equation can be accurately described by combining mode truncation and averaging methods, valid in the…
We present the results of linear stability of a damped coplanar double pendulum and its non-linear motion, when the point of suspension is vibrated sinusoidally in the vertical direction with amplitude $a$ and frequency $\omega $. A double…
It is well known that the two-dimensional (2D) nonlinear Schr\"odinger equation (NLSE) with the cubic-quintic (CQ) nonlinearity supports a family of stable fundamental solitons, as well as solitary vortices (alias vortex rings), which are…
This work explores the possibility of creating and controlling unconventional nonlinearities by periodic driving, in a broad class of systems described by the nonlinear Schr\"odinger equation (NLSE). By means of a parent quantum many-body…
In this contribution, we introduce numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, to the problem of tracing the parameter dependence of bound and resonant states…
The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its…
The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time PT symmetric potentials are considered. The model is relevant among others to experiments in optical…
We consider the stationary solutions for a class of Schroedinger equations with a symmetric double-well potential and a nonlinear perturbation. Here, in the semiclassical limit we prove that the reduction to a finite-mode approximation give…
Nonlinear Floquet states associated with a symmetry-breaking driving field are exploited to control the dynamics of a Bose-Einstein condensate in a double-well potential. The population imbalance between the two wells is shown to be…
In the present work, we study coherent structures in a one-dimensional discrete nonlinear Schr\"odinger lattice in which the coupling between waveguides is periodically modulated. Numerical experiments with single-site initial conditions…
Motivated by recent experimental studies of matter-waves and optical beams in double well potentials, we study the solutions of the nonlinear Schr\"{o}dinger equation in such a context. Using a Galerkin-type approach, we obtain a detailed…
The parametrically driven, damped nonlinear Schr\"odinger equation has two cn- and two dn-wave solutions. We show that one pair of the cn and dn solutions is unstable for any combination of the driver's strength, dissipation coefficient and…
Driving quantum materials with coherent light has proven a powerful platform to realize a plethora of interesting phases and transitions, ranging from ferroelectricity to superconductivity and limit cycles in pumped magnonics. In this paper…