相关论文: On multiscale Gevrey and q-Gevrey asymptotics for …

Linear second order differential equations having a large real parameter and turning point in the complex plane are considered. Classical asymptotic expansions for solutions involve the Airy function and its derivative, along with two…

We prove an ultrametric q-difference version of the Maillet-Malgrange theorem, on the Gevrey nature of formal solutions of nonlinear analytic q-difference equations. Since \deg_q and \ord_q define two valuations on {\mathbb C}(q), we…

We consider the Cauchy problem for the defocusing complex mKdV equation with finite density initial data \begin{align*} &q_t+\frac{1}{2}q_{xxx}-3|q|^2q_{x}=0,\\ &q(x,0)=q_{0}(x) \sim \pm 1, \ x\to \pm\infty, \end{align*} which can be…

We study higher-order asymptotic expansions of eigenvalues in perturbed transfer operators, of the corresponding eigenfunctions and of the corresponding eigenvectors of the dual operators. In our main result, we give explicit expressions of…

Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…

The number A(q) shows the asymptotic behaviour of the quotient of the number of rational points over the genus of non-singular absolutely irreducible curves over a finite field Fq. Research on bounds for A(q) is closely connected with the…

The purpose of this note is to share some observations and speculations concerning the asymptotic behavior of Gromov-Witten invariants. They may be indicative of some deep phenomena in symplectic topology that in full generality are outside…

This paper studies the Cauchy problem for variable coefficient weakly hyperbolic first order systems of partial differential operators. The hyperbolicity assumption is that for each $t, x$ the principal symbol is hyperbolic. No hypothesis…

We provide a quantitative version of a result due to Poffald and Reich on the asymptotic behavior of solutions of a second-order Cauchy problem generated by an accretive operator in the form of a rate of convergence. This quantitative…

We return to the subject of stability of infinite time asymptotics of kinetic equations. We found a model which is simpler than those studied previously and which shows unstable behavior corresponding to our arguments to appear elsewhere,…

We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…

We establish the asymptotic behavior of the Andrews $G_k(q)$ function as $q\to 1.$

We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…

This paper is devoted to the study of the singularly perturbed second order partial integro-differential equations. The estimation of the solutions of Cauchy problem is obtained.

In this paper we extend the umbral calculus, developed to deal with difference equations on uniform lattices, to q-difference equations. We show that many of the properties considered for shift invariant difference operators satisfying the…

In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing…

We study semiclassical Gevrey pseudodifferential operators, acting on exponentially weighted spaces of entire holomorphic functions. The symbols of such operators are Gevrey functions defined on suitable I-Lagrangian submanifolds of the…

In this paper, we improve and extend the results obtained by Boukarou et al. \cite{boukarou1} on the Gevrey regularity of solutions to a fifth-order Kadomtsev-Petviashvili-II equation. We establish Gevrey regularity in the time variable for…

The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…

In this paper we derive a sufficient condition for the existence of a unique solution of a Cauchy type q-fractional problem (involving the fractional q-derivative of Riemann-Liouville type) for some nonlinear differential equations. The key…