Related papers: A Nonlinear Adiabatic Theorem for Coherent States
The propagation of matter waves in curved geometry is relevant for electrons in nano-wires, solid-state physics structures and atomtronics. Curvature effects are usually addressed within the adiabatic limit and treated via an effective…
The nonlinear Schr\"odinger equation (NLSE) models the slowly varying envelope dynamics of a weakly nonlinear quasi-monochromatic wave packet in dispersive media. In the context of Bose-Einstein condensate (BEC), it is often referred to as…
We consider the cubic nonlinear Schr\"odinger equation with an exceptional potential. We obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions. We prove the existence of…
We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we…
The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at relatively small angle with respect to the…
We propose a mathematical framework to systematically explore the propagation properties of a class of continuous in time nonlinear neural network models comprising a hierarchy of processing areas, mutually connected according to the…
We report water wave experiments performed in a long tank where we consider the evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a large-scale rectangular barrier. Our experiments reveal that, for a…
The propagation of $N$ photons in one dimensional waveguides coupled to $M$ qubits is discussed, both in the strong and ultrastrong qubit-waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and…
Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based…
We rigorously derive multi-pulse interaction laws for the semi-strong interactions in a family of singularly-perturbed and weakly-damped reaction-diffusion systems in one space dimension. Most significantly, we show the existence of a…
We investigate beam diffraction and spatial modulation instability of coherent light beams propagating in the non-paraxial regime in a nonlinear Kerr medium. We study the instability of plane wave solutions in terms of the degree of…
We consider a class of nonlinear Schrodinger equation in four and five space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in L2)…
The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrodinger…
We investigate numerically by a conservative difference scheme in complex arithmetic the head-on and takeover collision dynamics of the solitary waves as solutions of linearly Coupled Nonlinear Schr\"odinger Equations for various initial…
We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists in a 1+1D generalized nonlinear Schr\"odinger equation with a periodic nonlinear…
We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many…
We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse…
We show that generalized coherent states follow Schr\"{o}dinger dynamics in time-dependent potentials. The normalized wave-packets follow a classical evolution without spreading; in turn, the Schr\"{o}dinger potential depends on the state…
We derive a non-linear supersymmetric sigma-model for the transport of light (classical waves) through a disordered medium. We compare this model with the well-established non-linear sigma-model for the transport of electrons (Schroedinger…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…