In this paper, we present a new method of deducing infinite sequences of exact solutions of q-discrete Painlevé equations by using their associated linear problems. The specific equation we consider in this paper is a q-discrete version of the [...]
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Multidimensional consistency has emerged as a key integrability property for partial difference equations (PEs) defined on the ‘space–time’ lattice. It has led, among other major insights, to a classification of scalar affine-linear [...] Since 1889, the international prototype of the kilogram has served to define the unit of mass in what is now known as the International System of Units (SI). This definition, which continues to serve mass metrology well, is an anachronism for [...] This article concerns the Weyl series of spectral functions associated with the Dirichlet Laplacian in a d-dimensional domain with a smooth boundary. In the case of the heat kernel, Berry and Howls predicted the asymptotic form of the Weyl series [...] A correct proof is given for the following assertions about the two-dimensional sloshing problem. The fundamental eigenvalue is simple and the corresponding stream function may be chosen to be non-negative in the closure of the water domain. New [...] We study an eigenvalue problem with a spectral parameter in a boundary condition. The problem describes sloshing of a heavy liquid in a container, which means that the unknowns are the frequencies and modes of the liquid’s free oscillations. [...] Relativistic and non-relativistic scattering by short-range potentials is investigated for selected problems. Scattering by the ‘ potential in the Schrödinger equation and potentials in the Dirac equation must be solved by regularization, [...] We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of low genus with many automorphisms, concentrating mostly on the case of genus 1 and 2. In the genus 1 case, we give addition formulae for the [...] |
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