The multiple scale expansion method is used to derive amplitude equations for a system with thermohaline convection in the neighborhood of Hopf and Taylor bifurcation points and at the double zero point of the dispersion relation. A complex Ginzburg-Landau equation, a Newell-Whitehead-type equation, and an equation of the φ type, respectively, were obtained. Analytic expressions for the coeffic...

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of GinzburgLandau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear...

Abstract. In this paper we establish the stability of Jensen’s functional equation on some classes of groups. We prove that Jensen equation is stable on noncommutative groups such as metabelian groups and T (2,K), where K is an arbitrary commutative field with characteristic different from two. We also prove that any group A can be embedded into some group G such that the Jensen functional equa...

We propose a novel shock-capturing method that is based on the ideas of characteristic filters and dynamic suboptimal control. A cost function is based on the smoothness of the solution, and formally minimized to obtain the unknown coefficient in the shock-capturing numerical fluxes. The proposed dynamic procedure is applied to one–dimensional Euler equation equation and two–dimensional Navier–...

The Makeenko-Migdal loop equation is non-linear and first order in the area derivative, but we show that for simple loops in QCD2 it is possible to reformulate this equation as a linear equation with second order derivatives. This equation is a bound state Schrödinger equation with a three dimensional Coulomb potential. Thus, loop dynamics leads to a surprising new picture of confinement, where...

For a system of noninteracting electrons scattered by neutral impurities, we derive a modified Boltzmann equation that includes quasiparticle and virial corrections. We start from a quasiclassical transport equation for nonequilibrium Green’s functions and apply a limit of small scattering rates. The resulting transport equation for quasiparticles has gradient corrections to scattering integral...

We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations. Two of the Rabelo equations are found to be related to the sine-Gordon equation. The other two are transformed into a linear equation and the Liouville equation, an...

In 1986, Mills and Robbins observed by computer the continued fraction expansion of certain algebraic power series over a finite field. Incidentally, they came across a particular equation of degree four in characteristic p = 13. This equation has an analogue for all primes p ≥ 5. There are two patterns for the continued fraction of the solution of this equation, according to the residue of p m...

In order to maximize the information that a linearized stability analysis provides, one should work with two free parameters rather than one. Moreover, it is recommended to first consider coefficients in the characteristic equation as parameters and in a second step (try to) invert the map that defines the coefficients in terms of the parameters as they occur in the original equation. Our aim i...

An eigenvalue based approach for the stabilization of linear neutral functional differential equations is presented, which extends the recently developed continuous pole placement method for delay equations of retarded type. The approach consists of two steps. First the stability of the associated difference equation is determined and a procedure is applied to compute the supremum of the real p...