Starting from an effective action for the order parameter field, we derive a coupled set of generalized hydrodynamic equations for a Bose condensate in an optical lattice at finite temperatures. Using the linearized hydrodynamic equations, we study the microscopic mechanism of the Landau instability due to the collisional damping process between condensate and noncondensate atoms. It is shown t...

We consider the following system of equations 8 < : A(x; t) has period L where > > 0. For any nite L, we completely classify the existence of solutions with minimal period and the stability and instability of all periodic solutions. 1. Introduction In this paper, we continue our study on the following amplitude equations which arise when expanding the problem in terms of fast and slow (or envel...

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solut...

The Casimir attraction can significantly interfere the physical response of nanoactuators. The intensity of the Casimir force depends on the geometries of interacting bodies. The present paper is dedicated to model the influence of the Casimir attraction on the electrostatic stability of nanoactuators made of cylindrical conductive nanowire/nanotube. An asymptotic solution, based on path-integr...

A two-population firing-rate model describing the dynamics of excitatory and inhibitory neural activity in one spatial dimension is investigated with respect to formation of patterns, in particular stationary periodic patterns and spatiotemporal oscillations. Conditions for existence of spatially homogeneous equilibrium states are first determined, and the stability properties of these equilibr...

The use of central differences on a rectangular net, in solving the primitive or vorticity equations, produces solutions on each of t.wo lattices. By exploring this lattice structure, a formal equivalence is established between the central-difference vorticity and primitive equations. A demonstration is given also that exponential instability previously found to result from certain types of bou...

We derive nonlocal coupled-mode equations for a Bragg grating embedded in a medium with nonlocal nonlinearity. Using these equations, we study the oscillatory instability of nonlocal Bragg solitary waves and demonstrate that collisions between them result in fusion into a standing pulse or breather , possibly with generation of additional jets, in a broad range of parameters. The results are ex...

We consider the mean eld theory of optimally pruned per-ceptrons. Using the cavity method, microscopic equations for the weights and the examples are derived. Their statistical properties agree with previous results using the replica method. There is a gap in the weight distribution, causing an instability in the ground state. A rough energy landscape better describes the learning problem. Solu...

Abstract: New physical principle for Monte-Carlo simulations has been introduced. It is based upon coupling of dynamical equations and the corresponding Liouville equation. The proposed approach does not require a random number generator since randomness is generated by instability of dynamics triggered and controlled by the feedback from the Liouville equation. Direct simulation of evolutionar...

We study the stability and instability of periodic traveling waves for Korteweg-de Vries type equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer for a suitable variational problem is nonlinearly stable to period preserving perturbations. We then discuss when the associated linearized equation admits solutions exponentiall...