Related papers: Averaging of Nonlinearity Management with Dissipat…
A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…
This paper is devoted to the averaged controllability of the random Schr\"odinger equation, with diffusivity as a random variable drawn from a general probability distribution. First, we show that the solutions to these random Schr\"odinger…
Integrable fractional equations such as the fractional Korteweg-deVries and nonlinear Schr\"odinger equations are key to the intersection of nonlinear dynamics and fractional calculus. In this manuscript, the first discrete/differential…
We investigate the soliton dynamics for the fractional nonlinear Schrodinger equation by a suitable modulational inequality. In the semiclassical limit, the solution concentrates along a trajectory determined by a Newtonian equation…
We give a survey on recent developments on nonlinear Schr\"odinger equations with dissipative structure based on the authors' recent works.
The Nonlinear Schroedinger Equation (NLSE) with a random potential is motivated by experiments in optics and in atom optics and is a paradigm for the competition between the randomness and nonlinearity. The analysis of the NLSE with a…
A stochastic differential equation for the plasma density dynamics is derived, consistent with the experimentally measured distribution and the theoretical quadratic nonlinearity. The plasma density is driven by a multiplicative Wiener…
In this paper, we present a novel stochastic and spatially lumped multi-mode model to describe the nonlinear dynamics of actively Q-switched lasers and random perturbations due to amplified spontaneous emission. This model will serve as a…
We consider the dispersion managed nonlinear Schr\"dinger equations with quintic and cubic nonlinearities in one and two dimensions, respectively. We prove the global well-posedness and scattering in $L_x^2$ for small initial data employing…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
The existence of ``dispersion-managed solitons'', i.e., stable pulsating solitary-wave solutions to the nonlinear Schr\"{o}dinger equation with periodically modulated and sign-variable dispersion is now well known in nonlinear optics. Our…
We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a…
We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a…
This paper addresses the problem of averaged controllability for the time-fractional Schrodinger equation, where the quantum diffusivity parameter is a random variable with a general probability distribution. First, by exploiting the…
We study the violation of the adiabaticity of the electron dynamics in a slowly varying magnetic field. We formulate and solve exactly a non-adiabatic scattering problem. In particular, we consider scattering on a magnetic field…
By considering a solvable driven-dissipative quantum model, we demonstrate that continuous second order phase transitions in dissipative systems may occur without an accompanying spontaneous symmetry breaking. As such, the underlying…
In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a…
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…
Dissipation anomaly-the persistence of finite energy dissipation in the inviscid limit-is a hallmark of turbulence, sometimes regarded as the "zeroth law" of turbulent flows. Here, we demonstrate that this phenomenon is not exclusive to…