Related papers: Dromion perturbation for the Davey-Stewartson-1 eq…
We study the structure of the set of harmonic solutions to perturbed nonautonomous, T-periodic, separated variables ODEs on manifolds. The perturbing term is allowed to contain a finite delay and to be T-periodic in time.
We discuss stability of the first eigenvalue of the 1-Laplacian under perturbations of the domain.
In this paper we discuss properties of the KdV equation under periodic boundary conditions, especially those which are important to study perturbations of the equation. Next we review what is known now about long-time behaviour of solutions…
We study, by means of a topological approach, the forced oscillations of second order functional retarded differential equations subject to periodic perturbations. We consider a delay-type functional dependence involving a gamma probability…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
This work is devoted to study the relation between regularity and decay of solutions of some dissipative perturbations of the Korteweg-de Vries equation in weighted and asymmetrically weighted Sobolev spaces.
We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated random velocity field. We carry on an expansion in powers of the inverse square…
A perturbation method is presented which can be applied to the description of a wide range of physical problems that deal with dynamics of dipolar coupled spins in solids. The method is based on expansion of the operator exponent in a…
An efficient high precision hybrid numerical approach for integrable Davey-Stewartson (DS) I equations for trivial boundary conditions at infinity is presented for Schwartz class initial data. The code is used for a detailed numerical study…
We study the evolution of the energy (mode-power) distribution for a class of randomly perturbed Hamiltonian partial differential equations and derive {\it master equations} for the dynamics of the expected power in the discrete modes. In…
Perturbations around autonomous one-dimensional single-species reaction-diffusion systems are investigated. It is shown that the parameter space corresponding to the autonomous systems is divided into two parts: In one part, the system is…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic…
The peculiar intergrability of the Davey-Stewartson equation allows us to find analytically solutions describing the simultaneous formation and interaction of one-dimensional and two-dimensional localized coherent structures. The predicted…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
This work is concerned with the stability of regime-switching processes under the perturbation of the transition rate matrices. From the viewpoint of application, two kinds of perturbations are studied: the size of the transition rate…
A very efficient large-order perturbation theory is formulated for the nuclear motion of a linear triatomic molecule. To demonstrate the method, all of the experimentally observed rotational energies, with values of $J$ almost up to 100,…
In this article, a perturbation theory of the compressible Navier-Stokes equations in $\mathbb{R}^n$ $(n \geq 3)$ is studied to investigate decay estimate of solutions around a non-constant state. As a concrete problem, stability is…
In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.
I discuss a recent application of homotopy perturbation and Adomian decomposition methods to the linear and nonlinear Schr\"odinger equations. I propose a generalization of the procedure for the treatment of a wider class of problems.
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…