Related papers: Condensation in disordered lasers: theory, 3D+1 si…
The statistical properties of the phases of several modes nonlinearly coupled in a random system are investigated by means of a Hamiltonian model with disordered couplings. The regime in which the modes have a stationary distribution of…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
Small parts of the electronic wavepacket of a multiple charged ion may still tunnel through the high Coulomb barrier for a sufficiently intense laser field of $10^{15}W/cm^2$ and higher. Solving numerically the corresponding Schr\"odinger…
The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation,…
These notes contain a rapid overview of the methods and results obtained in the field of propagation of waves in disordered media. The case of Schr\"odinger and Helmholtz equations are considered that describe respectively electrons in…
The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…
We measure spectra, spatial correlation functions and probability density functions (PDFs) for waves amplitudes for generalized one-dimensional nonlinear Schrodinger (NLS) equation of focusing type with saturated nonlinearity. All…
In this work we present a method for generating random matrices describing electromagnetic scattering from disordered media containing dielectric particles with prescribed single particle scattering characteristics. Resulting scattering…
We derive several kinetic equations to model the large scale, low Fresnel number behavior of the nonlinear Schrodinger (NLS) equation with a rapidly fluctuating random potential. There are three types of kinetic equations the longitudinal,…
The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the…
We consider the 3-dimensional nonlinear Schr\"{o}dinger equation (NLS) with average nonlinearity. This is a limiting model of NLS with strong magnetic confinement and a generalized model of the resonant system of NLS with a partial harmonic…
A two-dimensional generalized cubic nonlinear Schr\"odinger equation with complex coefficients for the group dispersion and nonlinear terms is used to investigate the evolution of a finite-amplitude localized initial perturbation. It is…
We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…
We investigate mode-locking processes in lasers displaying a variable degree of structural randomness, from standard optical cavities to multiple-scattering media. By employing methods mutuated from spin-glass theory, we analyze the…
Excitable waves arise in many spatially-extended systems of either biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the…
We present a theoretical study of the temporal and spatial coherence properties of a topological laser device built by including saturable gain on the edge sites of a Harper--Hofstadter lattice for photons. For small enough lattices the…
Soliton strings in mode-locked lasers are obtained using a variant of the nonlinear Schrodinger equation, appropriately modified to model power (intensity) and energy saturation. This equation goes beyond the well-known master equation…
We study the possibility to create many-particle Schr\"odinger cat-like states by using a Feshbach resonance to reverse the sign of the scattering length of a Bose-Einstein condensate trapped in a double-well potential. To address the issue…
A numerical exploration of a gain-loss nonlinear Schr\"odinger equation was carried out utilizing over 180000 core hours to conduct more than 10000 unique simulations in an effort to characterize the model's six dimensional parameter space.…
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…