Related papers: Chaoticons described by nonlocal nonlinear Schrodi…
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger…
We analyze the chaotic dynamics of a one-dimensional discrete nonlinear Schr\"odinger equation. This nonintegrable model, ubiquitous in several fields of physics, describes the behavior of an array of coupled complex oscillators with a…
The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…
Binary discrete nonlinear Schr\"odinger equation is used to describe dynamics of two-species Bose-Einstein condensate loaded into an optical lattice. Linear inter-species coupling leads to Rabi transitions between the species. In the regime…
The chaotic scattering theory is here extended to obtain escape-rate expressions for the transport coefficients appropriate for a simple classical fluid, or for a chemically reacting system. This theory allows various transport coefficients…
Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e., globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible…
We construct quasi-periodic solutions to the lattice nonlinear random Schroedinger equation on a set of potentials of positive measure via using a Lyapunov-Schmidt decomposition and a multiscale Newton scheme.
A conjecture connecting Lyapunov exponents of coupled map lattices and the node theorem is presented. It is based on the analogy between the linear stability analysis of extended chaotic states and the Schr\"odinger problem for a particle…
This thesis focuses on the mechanisms of energy transport in multidimensional heterogeneous lattice models, studying in particular the case of the Klein-Gordon model of coupled anharmonic oscillators in one and two spatial dimensions. We…
In this paper, we give a proof of the existence of stationary dark soliton solutions or heteroclinic orbits of nonlinear equations of Schr\"odinger type with periodic inhomogeneous nonlinearity. The result is illustrated with examples of…
Chaos as typical property of non-linear systems has revealed its crucial role in various problems of astrophysics and cosmology. The problems discussed at these lectures include planetary dynamics, galactic dynamics, reconstruction of the…
Intermittent high-amplitude structures emerge in a damped and driven discrete nonlinear Schroedinger equation whose solutions transport both energy and particles from sources to sinks. These coherent structures are necessary for any…
Cross section fluctuations in nuclear scattering are briefly reviewed in order to show the main important features. Then chaotic scattering is introduced by means of a very simple model. It is shown that chaoticity produces the same kind of…
Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in…
In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…
Nonlinear Schr\"odinger equation, complemented by a confining potential, possesses a discrete set of stationary solutions. These are called coherent modes, since the nonlinear Schr\"odinger equation describes coherent states. Such modes are…
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's…
The Discrete Nonlinear Schroedinger Equation with a random potential in one dimension is studied as a dynamical system. It is characterized by the length, the strength of the random potential and by the field density that determines the…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…