Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this paper, a single-phase soliton-form solution of the Korteweg-de Vries equation with variable coefficients is presented, and the Dirichlet series for constructing asymptotic expansions for general equations.
Abstract: CONTENTSIntroductionChapter I. The Korteweg-de Vries equation with variable coefficients § 1. Basic definitions. A single-phase soliton-form solution of the Korteweg-de Vries equation with variable coefficients § 2. Construction of an asymptotic single-phase soliton-form solution § 3. Conservation lawsChapter II. The Kadomtsev-Petviashvili equation and the sine-Gordon equation § 1. The Kadomtsev-Petviashvili equation § 2. The sine-Gordon equation with variable coefficientsChapter III. Multi-phase asymptotic solutions of non-linear equations and Dirichlet series § 1. Multi-phase asymptotic solutions § 2. Dirichlet series for constructing asymptotic expansions for general equationsReferences
102 citations
•
01 Nov 1991101 citations
••
100 citations
••
100 citations
••
01 Jan 1989
TL;DR: An asymptotic formula is a form of a function that approximates the value of the integrand and its derivatives at a finite number of points, or in terms of some simpler integral as discussed by the authors.
Abstract: An asymptotic formula or asymptotic form for a function f(x) is the name usually given to an approximate formula f(x) ≈ g(x) in some domain of values of x, where g(x) is ‘simpler’ then f(x). For example, if f(x) is an integral, then g(x) must either be given in terms of the values of the integrand and its derivatives at a finite number of points, or in terms of some simpler integral. If f(x) is a solution of an ordinary differential equation, then g(x) must either be expressed in quadratures or be the solution of a ‘simpler’ differential equation. This list can be extended—there is an unwritten heirarchy of asymptotic formulae. Of course all these definitions are very blurred. ‘“What is asymptotics?” This question is about as difficult to answer as the question “What is mathematics?”’
99 citations