Related papers: Exponential asymptotics and higher-order Stokes ph…
The computation of the amplitude, $\alpha$, of asymptotic standing wave tails of weakly delocalized, stationary solutions in a fifth-order Korteweg-de Vries equation is revisited. Assuming the coefficient of the fifth order derivative term,…
In the present work, we revisit the topic of translational eigenmodes in discrete models. We focus on the prototypical example of the discrete nonlinear Schr{\"o}dinger equation, although the methodology presented is quite general. We…
An enriched hybrid high-order method is designed for the Stokes equations of fluid flow and is fully applicable to generic curved meshes. Minimal regularity requirements of the enrichment spaces are given, and an abstract error analysis of…
First approach of invariant densities of a Perron Frobenius operator. Asymptotic behaviours of ODE or PDE, as, are most interesting. The associed infinitesimal iteration is. If is partially linear, a random distribution can be asymptotic…
In this work we propose a new method for investigating connection problems for the class of nonlinear second-order differential equations known as the Painlev{\'e} equations. Such problems can be characterized by the question as to how the…
We present how a probabilistic model can describe the asymptotic behavior of the iterations, with applications for ODE and approach of some problems in mechanics in $\mathbb{R}^d$.
The asymptotic representations of the functions ${\rm Ai}_1(x), {\rm Gi}(x), {\rm Ai}'(x), {\rm Ai}^2(x), {\rm Bi}^ 2(x)$ are obtained. As a by-product, the factorial identity (21') is found. The derivation of asymptotic representations of…
The use of hyperasymptotics and the Weniger transformation has been proposed, in a joint fashion, for decoding the divergent asymptotic series generated by the steepest descent on a wide class of saddle-point integrals {evaluated across…
The Stokes wave problem in a constant vorticity flow is formulated, by virtue of conformal mapping techniques, as a nonlinear pseudodifferential equation, involving the periodic Hilbert transform, which becomes the Babenko equation in the…
A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.
We study the full asymptotic expansion of the monodromy data ({\it i.e.}, Stokes multipliers) for the first Painlev\'{e} transcendent (PI) with large initial data or large pole parameters. Our primary approach involves refining the complex…
We classify the local asymptotic behavior of positive singular solutions to a class of subcritical sixth order equations on the punctured ball. Initially, using a version of the integral moving spheres technique, we prove that solutions are…
For equation P$_I^2$, the second member in the P$_I$ hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $t$ and evaluate the asymptotics in the complex $x$ plane for $|x|\to\infty$ and…
Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the…
We give a new global presentation of our results on the asymptotic behavior of an iteration. This paper brings many improvements and corrections to our previous preprints on the subject. Among the applications, we use new methods to compute…
Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. However, the theoretical aspects, e.g., identifiability and asymptotic properties of statistical estimation are still obscure. This paper…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear…
Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on {\em analytically-solvable}…
A random composition of $n$ appears when the points of a random closed set $\widetilde{\mathcal{R}}\subset[0,1]$ are used to separate into blocks $n$ points sampled from the uniform distribution. We study the number of parts $K_n$ of this…