Related papers: On Baxter's difference systems
The variance of the number of lattice points inside the dilated bounded set rD with random position in R^d has asymptotics r^(d-1) if the rotational quadratic average of the modulus of the Fourier transform of the set is O(r^(-d-1)). The…
Purely numerical methods do not always provide an accurate way to find all the global solutions to nonlinear ODE on infinite intervals. For example, finite-difference methods fail to capture the asymptotic behavior of solutions, which might…
The main subject of the paper is the so-called Discrete Painlev\'e-1 Equation (DP1). Solutions of DP1 are classified under criterion of their behavior while argument tends to infinity. The Isomonodromic Deformations Method yields asymptotic…
This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…
One discusses a problem of asymptotical behavior for some operators in a general theory of pseudo differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit representations for these…
We derive bilateral asymptotic as well as non-asymptotic estimates for the multivariate Laplace integrals. Possible applications: Tauberian theorems for random vectors.
The classical Lorenz lowest order system of three nonlinear ordinary differential equations, capable of producing chaotic solutions, has been generalized by various authors in two main directions: (i) for number of equations larger than…
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…
In this paper we propose algebraic universal procedure for deriving "fusion rules" and Baxter equation for any integrable model with $U_q(\widehat{sl}_2)$ symmetry of Quantum Inverse Scattering Method. Universal Baxter Q- operator is got…
By considering the nonuniform exponential dichotomy spectrum, we introduce a global asymptotic nonuniform stability conjecture for nonautonomous differential systems, whose restriction to the autonomous case is related to the classical…
We consider the generalised Beta function introduced by Chaudhry {\it et al.\/} [J. Comp. Appl. Math. {\bf 78} (1997) 19--32] defined by \[B(x,y;p)=\int_0^1 t^{x-1} (1-t)^{y-1} \exp \left[\frac{-p}{4t(1-t)}\right]\,dt,\] where $\Re (p)>0$…
The existence of a formal particular solution (family of solutions) of oscillating type under certain conditions has been proved for the quasi-linear ordinary differential equations system. The asymptotic nature of this solution (the family…
The work is devoted to the construction of the asymptotic behavior of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends…
We analyze the spatial structure of asymptotics of a solution to a singularly perturbed system of mass transfer equations. The leading term of the asymptotics is described by a parabolic equation with possibly degenerate spatial part. We…
We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…
We study the spectra for a class of differential operators with asymptotically constant coefficients.These operators widely arise as the linearizations of nonlinear partial differential equations about patterns or nonlinear waves. We…
A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients has the form $t^{-\alpha}a(t)$,~$\alpha>0$, where $a(t)$ is trigonometric polynomial with an arbitrary set of frequencies.…
In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $ D^{\alpha}_Cu(t)=Au(t)+f(t), u(0)=x, 0<\alpha\le1, ( *) $ where $D^{\alpha}_Cu(t)$ is the derivative of the function $u$ in the…
Results of investigation of the asymptotic behavior of solutions to the Cauchy problems for a quasi-linear parabolic equation with a small parameter at a higher derivative near singular points of limit solutions are presented. Interest to…
The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton-Maclaurin expansion. Several basic…