We study a new class of kinetic equations describing nonequilibrium macroscopic dynamics of soliton gases with elastic collisions. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of N -component ‘cold-gas’ hydrodynamic reductions. We prove that these reductions represent integrable linearly degener...

in this paper, we try to use modeling based on singular perturbation theory, in order to control satellite attitude during the wide rolling angle maneuvering through nonlinear h∞ control strategy. differential equations describing dynamics of the satellite are presented first, and by choosing the appropriate dynamic model for actuators and based on the standard singular perturbation model, the ...

Presented is a quantum lattice gas for Navier-Stokes fluid dynamics simulation. The quantum lattice-gas transport equation at the microscopic scale is presented as a generalization of the classical lattice-gas transport equation. A special type of quantum computer network is proposed that is suitable for implementing the quantum lattice gas. The quantum computer network undergoes a partial coll...

A new approach to the design of flux-corrected transport (FCT) algorithms for linear/bilinear finite element approximations of convection-dominated transport problems is pursued. The raw antidiffusive fluxes are linearized about an intermediate solution computed by a positivity-preserving low-order scheme. By virtue of this linearization, the costly evaluation of correction factors needs to be ...

In this paper we consider the nonlinear Schrr odinger equation with an oscillatory, mean-zero dispersion, which has recently been proposed as an alternative method of dispersion compensation for pulse transmission in optical bers. Under the assumption that the time scale on which the dispersion changes is short in comparison with the dispersion and nonlinearity time scales, we are able to facto...

We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy [10, 11] extends to the threshold energy in...

Conditions for Global Asymptotic Stability (GAS) of a nonlinear relaxation equation realised by a Nonlinear Autoregressive Moving Average (NARMA) recurrent perceptron are provided. Convergence is derived through Fixed Point Iteration (FPI) techniques, based upon a contraction mapping feature of a nonlinear activation function of a neuron. Furthermore, nesting is shown to be a spatial interpreta...

We consider the Bose–Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes — a nonlinear generalisation of the (symmetric and antisymmetric) Hermite–Gauss eigenmodes of a harmonic quantum oscillator.  2001 Elsevier Science B.V. All rights reserved. PACS: 03.75.F; 03.75.-b; 03.50.-z; 73.20.Dx The recent obser...