Related papers: On the precise cusped behaviour of extreme solutio…
Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an…
In this work, we develop a linear model ODE to study the parasitic capillary ripples present on steep Stokes waves when a small amount of surface tension is included in the formulation. Our methodology builds upon the exponential asymptotic…
Travelling waves in woodpile chains are typically nanoptera, which are composed of a central solitary wave and exponentially small oscillations. These oscillations have been studied using exponential asymptotic methods, which typically…
We consider fluid flows for which the linearized Navier-Stokes operator is strongly non-normal. The responses of such flows to external perturbations are spanned by a generically very large number of non-orthogonal eigenmodes. They are…
We consider propagation of instability fronts in conservative nonlinear wave systems by the Whitham method. Whitham modulation equations for periodic solutions of the generalized Klein-Gordon equation are solved in the limit of…
In this paper, we develop a new strategy aimed at obtaining high-order asymptotic models for transport equations with highly-oscillatory solutions. The technique relies upon recent developments averaging theory for ordinary differential…
When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…
The precise asymptotic behaviour of the solutions to the twodimensional curvature equation $\Delta u=k(z) e^{2 u}$ with $e^{2 u} \in L^1$ for bounded nonnegative curvature functions $-k(z)$ near isolated singularities is obtained.
We study periodic, two-dimensional, gravity-capillary traveling wave solutions to a viscous shallow water system posed on an inclined plane. While thinking of the Reynolds and Bond numbers as fixed and finite, we vary the speed of the…
The paper concerns the problem for the ultrahyperbolic equation in the Euclidean space with data on a characteristic hyperplane. Smoothness and asymptotics of the solution along characteristic lines transversal to the initial hyperplane are…
In this paper, we study the asymptotic behavior of solutions to the wave equation with damping depending on the space variable and growing at the spatial infinity. We prove that the solution is approximated by that of the corresponding heat…
Semiclassical asymptotics for linear Schr\"odinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment…
In this paper, we investigate the long time behaviour for a class of low-regularity solutions of the Camassa-Holm equation given by the superposition of infinitely many interacting traveling waves with corners at their peaks.
We consider the asymptotic behaviour of small-amplitude gravity water waves in a rectangular domain where the water depth is much smaller than the horizontal scale. The control acts on one lateral boundary, by imposing the horizontal…
We apply an extension of a new method of group classification to a family of nonlinear wave equations labelled by two arbitrary functions, each depending on its own argument. The results obtained confirm the efficiency of the proposed…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
We study the large time behavior of solutions of first-order convex Hamilton-Jacobi Equations of Eikonal type set in the whole space. We assume that the solutions may have arbitrary growth. A complete study of the structure of solutions of…
We consider the existence and spectral stability of nonlinear discrete localized solutions representing light pulses propagating in a twisted multi-core optical fiber. By considering an even number, $N$, of waveguides, we derive asymptotic…
We are concerned with minimax signal detection. In this setting, we discuss non-asymptotic and asymptotic approaches through a unified treatment. In particular, we consider a Gaussian sequence model that contains classical models as special…
In this article we study two classical linear water wave problems, i) normal modes of infinite straight channels of bounded constant cross-section, and ii) trapped longitudinal modes in domains with unbounded constant cross-section. Both…