Related papers: Dromion perturbation for the Davey-Stewartson-1 eq…

Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed in unique, simple and consistent manner. It has been shown that this theory is extended consistently to time-harmonic…

A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…

The nonlinear Vlasov equation contains the full nonlinear dynamics and collective effects of a given Hamiltonian system. The linearized approximation is not valid for a variety of interesting systems, nor is it simple to extend to higher…

We study the dispersion of a particle whose motion dynamics can be described by a forced velocity jump process. To investigate large deviations results, we study the Chapman-Kolmogorov equation of this process in the hyperbolic scaling…

Purely dispersive partial differential equations as the Korteweg-de Vries equation, the nonlinear Schr\"odinger equation and higher dimensional generalizations thereof can have solutions which develop a zone of rapid modulated oscillations…

Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.

In this article, we prove Carleman estimates for the generalized time-fractional advection-diffusion equations by considering the fractional derivative as perturbation for the first order time-derivative. As a direct application of the…

We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrodinger equations with gauge invariant power-law nonlinearities and non-local perturbations. The model includes the Davey--Stewartson…

The main aim of this paper is the investigation of the stability problem for ordinary delay differential equations. More precisely, we would like to study the following problem. Assume that for a continuous function a given delay…

The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study…

We study the spin-wave dispersion of localized spins in a disordered double-exchange model using the perturbation theory with respect to the strength of the disorder potential. We calculate the dispersion upto the next-leading order, and…

We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the…

Here, the perturbation equation for a dissipative medium is derived from the first principle from the linearized compressible Navier-Stokes equation without Stokes's hypothesis. The dispersion relations of this generic governing equation…

This paper concerns the large-time behavior of perturbations around a time-periodic solution to the Navier-Stokes-Fourier system in the three-dimensional whole space. The time-periodic solution exists when a given external force is small…

Computing the first few singular vectors of a large matrix is a problem that frequently comes up in statistics and numerical analysis. Given the presence of noise, exact calculation is hard to achieve, and the following problem is of…

We investigate the effect of time-dependent noise on the shape of a morphogen gradient in a developing embryo. Perturbation theory is used to calculate the deviations from deterministic behavior in a simple reaction-diffusion model of…

The discrete self-trapping equation (DST) represents an useful model for several properties of one-dimensional nonlinear molecular crystals. The modulational instability of DST equation is discussed from a statistical point of view,…

This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…

This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…

The construction of perturbation series for slightly deformed dielectric circular cavity is discussed in details. The obtained formulae are checked on the example of cut disks. A good agreement is found with direct numerical simulations and…