In this paper we study synchronization phenomena of spin-torque oscillators coupled on a ring. Spin-torque are nanoelectronic devices that promise efficient microwave generation provided they synchronized in large arrays. Due to their nonlinear and non-isochronous nature, properties difficult analyse explicitly. To address challenge, employ recently developed continuation method transform the n...

Burgers equation is a simplified form of the Navier-Stokes equation that represents the non-linear features of it. In this paper, the transient two-dimensional non-linear Burgers equation is solved using the Lattice Boltzmann Method (LBM). The results are compared with the Modified Local Crank-Nicolson method (MLCN) and exact solutions. The LBM has been emerged as a new numerical method for sol...

We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1//n-m/alpha+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order alpha, when 0<alpha<2. We consider a few mode...

We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction defined by a term proportional to 1/jn mj. Continuous medium equation for this system can be obtained in the socalled infrared limit when the wave number tends to zero. We construct a transform operator that maps the system of large number of ordinary differential equations of mot...

We use Elie Cartan's method of equivalence to give a complete classification, in terms of differential invariants, of second-order ordinary differential equations admitting Lie groups of fibre-preserving point symmetries. We then apply our results to the determination of all second-order equations which are equivalent, under fibre-preserving transformations, to the free particle equation. In ad...

This article is devoted to define and solve an evolution equation of the form dyt = ∆yt dt + dXt(yt), where ∆ stands for the Laplace operator on a space of the form L(R), and X is a finite dimensional noisy nonlinearity whose typical form is given by Xt(φ) = ∑N i=1 x i tfi(φ), where each x = (x , . . . , x) is a γ-Hölder function generating a rough path and each fi is a smooth enough function d...

We study the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space-time, energy fluctuations diffuse and evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for t...

In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...