We point out a close relation between a family of Gödel-type solutions of 3+1 General Relativity and the Landau problem in S2,R2 and H2; in particular, the classical geodesics correspond to Larmor orbits in the Landau problem. We discuss the extent of this relation, by analyzing the solutions of the Klein-Gordon equation in these backgrounds. Guided by the analogy with the Landau problem, we sp...

Spatially localized, time-periodic structures are common in pattern-forming systems, appearing in fluid mechanics, chemical reactions, and granular media. We examine the existence of oscillatory localized states in a PDE model with single frequency time dependent forcing, introduced in [22] as phenomenological model of the Faraday wave experiment. In this study, we reduce the PDE model to the f...

An important progress was recently done in numerical approximation of weak solutions to a micromagnetic model equation. The problem with the nonconvex sideconstraint of preserving the length of the magnetization was tackled by using reduced integration. Several schemes were proposed and their convergence to weak solutions was proved. All schemes were derived from the Landau-Lifshitz-Gilbert for...

‎in this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear pdes in mathmatical physics; namely the one-‎dimensional modified complex ginzburg-landau equation by using the $ (g^{'}/g) $ expansion method‎, homogeneous balance method, extended f-expansion method‎. ‎by ‎using homogeneous balance principle and the extended f-expansion, more periodic wave solutions expres...

f0(v) log f0(v)dv for all t ≥ 0. Assume that in a dilute gas or plasma, particles collide by pairs, due to a repulsive force proportional to 1/r, where r stands for the distance between the two particles. Then if s ∈ (2,∞), the velocity distribution solves the corresponding Boltzmann equation [14, 15]. But if s = 2, the Boltzmann equation is meaningless [14] and is often replaced by the Landau ...

Abstract The Landau–Lifshitz (LL) equation has been proposed as the classical to describe dynamics of a charged particle in strong electromagnetic field when influenced by radiation reaction. Until recently, there no clear experimental verification. However, aligned crystals have remedied situation: here, Nielsen et al CERN NA63 Collaboration (2020 Phys. Rev. D 102 052004), we report on quantit...

In this paper, two methods are employed to investigate for which values of the parameters, if any, the two-dimensional real Landau-Ginzburg equation possesses the Painlevé property. For an ordinary differential equation to have the Painlevé property, all of its solutions must be meromorphic but for partial differential equations there are two inequivalent definitions, one a direct investigation...