We show that continuous-time chaos can be defined using linear dynamics and represented by an exact analytic solution. A driven linear differential equation is used to define a low-dimensional chaotic set of continuous-time waveforms. A nonlinear differential equation is derived for which these waveforms are exact analytic solutions. This nonlinear system describes a chaotic semiflow with a ret...

The spectrum of a Schrödinger operator with a perfect honeycomb lattice potential has special points, called Dirac points where the lowest two branches of the spectrum touch. Deformations can result in the merging and disappearance of the Dirac points and the originally intersecting dispersion relation branches separate. Corresponding to these deformations, nonlinear envelope equations are deri...

A nonlinear equation describing curved stationary flames with arbitrary gas expansion θ = ρfuel/ρburnt, subject to the Landau-Darrieus instability, is obtained in a closed form without an assumption of weak nonlinearity. It is proved that in the scope of the asymptotic expansion for θ → 1, the new equation gives the true solution to the problem of stationary flame propagation with the accuracy ...

in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

This paper presents a numerical investigation of the laminar mixed convection flow of a radiating gas in an inclined lid-driven cavity. The fluid is treated as a gray, absorbing, emitting, and scattering medium. The governing differential equations including continuity, momentum and energy are solved numerically by the computational fluid dynamics techniques (CFD) to obtain the velocity and tem...

A nonlinear electrical transmission line with an intersite circuit element acting as a nonlinear resistance is introduced and investigated. In the continuum limit, the dynamics of localized signals is described by a nonlinear evolution equation belonging to the family of nonlinear diffusive Burgers’ equations. This equation admits compact pulse solutions and shares some symmetry properties with...

At low temperature, the equation of motion' for the spin density m in nuclear polarized paramagnetic liquids (e.g. , liquid He, HeHe mixtures) and gases (e.g. , He, H i ) differs from the conventional Fick's law form Bm/t)t =D V' m of classical systems. In general, the equation becomes nonlinear and anisotropic and the transverse component has an oscillatory (wave) as well as a diffusive charac...

The basis for a hydrodynamic description of granular gases is discussed for a low density gas of smooth, inelastic hard spheres. The more fundamental mesoscopic description is taken to be the nonlinear Boltzmann kinetic equation. Two arguments are presented in favor of a hydrodynamics for granular gases. The first one is the concept of a ”normal” solution and its explicit approximate constructi...