We develop an effective theory of pulse propagation in a nonlinear and disordered medium in two dimensions. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena which we refer to as "locked explosion" and diffusive collapse. The equation can be applied to such distinct physical systems as laser beams propaga...

Nonlinear evolution equation for Alfv6n waves, propagating in streaming plasmas with nonuniform densities and inhomogeneous rnag[letic fielcls, is obtained by using reductive perturbation technique. Numerical solution of this equation, which is a modified derivative nonlinear Schroclinger (MDNLS) equation, shows that the inhomogeneities exhibit their presence as the dissipation. ~’he evolution,...

The interaction of a weakly nonlinear Alfvénic pulse with an Alfvén speed inhomogeneity in the direction perpendicular to the magnetic field is investigated. Identically to the phase mixing experienced by a harmonic Alfvén wave, sharp transverse gradients are generated in the pulse by the inhomogeneity. In the initial stage of the evolution of an initially plane Alfvénic pulse, the transverse g...

Disordered soft materials, such as fibrous networks in biological contexts, exhibit a nonlinear elastic response. We study such nonlinear behavior with a minimal model for networks on lattice geometries with simple Hookian elements with disordered spring constant. By developing a mean-field approach to calculate the differential elastic bulk modulus for the macroscopic network response of such ...

Theories which have been used to describe the quantized electromagnetic field interacting with a nonlinear dielectric medium are either phenomenological or derived by quantizing the macroscopic Maxwell equations. Here we take a different approach and derive a Hamiltonian describing interacting fields from from one which contains both field and matter degrees of freedom. The medium is modelled a...

In this paper we study a porous medium equation with a nonlinear absorption term and a nonlinear boundary condition. We prove existence of weak solutions and also we establish some uniqueness and non uniqueness results for certain range of the parameters that appear in the problem. Finally we deal with the existence of global solutions in time or blow-up. We find in which region of parameters t...

We demonstrate the existence of noise-induced periodicity (coherence resonance) in both a discrete-time model and a continuous-time model of an excitable neuron. In particular, we show that the effects of noise added to the fast and slow dynamics of the models are dramatically different. A Fokker-Planck analysis gives a quantitative explanation of the effects. The effects of noise on nonlinear ...

We consider dynamical systems that are equivariant under a noncompact Lie group of symmetries and the drift of relative equilibria in such systems In particular we investigate how the drift for a parametrized family of normally hyperbolic relative equilibria can change character at what we call a drift bifurcation To do this we use results of Arnold to analyze parametrized families of elements ...

We describe the development and implementation of a family of non-linear filters in which the non-linear term is given a variable recursive delay, in the context of a search for what we term an arithmetical instrument – an instrument whose design is founded on purely numerical models. Such filters are inherently unstable; we describe how they may be controlled, not only by the careful selection...