Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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01 Jan 1986TL;DR: In this article, the degeneracy of the action in gauge theory has been studied in the context of logarithmic correction to the mean field picture in statistical mechanics models, which can be applied to any asymptotically free field theory provided one overcomes the difficulties linked to the formalism.
Abstract: As I said in the introduction, this method can clearly be extended to any asymptotically free field theory provided one overpasses the difficulties linked to the formalism (as for example the degeneracy of the action in gauge theory). It can also be applied to study logarithmic correction to the mean field picture in statistical mechanics models.
1 citations
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TL;DR: In this article, it was shown that the positive momentum density of the Camassa-Holm equation is a combination of Dirac measures supported on the positive axis, and that as time goes to infinity, the momentum density concentrates in small intervals moving right with different constant speeds.
Abstract: The paper addresses the asymptotic properties of Camassa-Holm equation on the half-line. That is, using the method of asymptotic density, under the assumption that it is unique, the paper proves that the positive momentum density of the Camassa-Holm equation is a combination of Dirac measures supported on the positive axis. This means that as time goes to infinity, the momentum density concentrates in small intervals moving right with different constant speeds.
1 citations
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TL;DR: In this article, the authors considered the problem of constructing asymptotic expansions of the solutions of integral equations of the second kind depending on a small parameter ϵ 〉 0 in such a way that the kernel of the integral operator has the nature of a δ-function.
Abstract: WE consider the problem of constructing asymptotic expansions of the solutions of integral equations of the second kind depending on a small parameter ϵ 〉 0 in such a way that as ϵ 〉 0 the kernel of the integral operator has the nature of a δ-function. It is proved that under certain conditions a boundary layer effect arises, and an iterative process is given for constructing the asymptotic expansion of the solution.
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TL;DR: The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered in this article, where the well-posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of the KG equation.
Abstract: The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered. Firstly, using the contraction mapping principle, combining some priori estimates and the convergence of Bessel function, the well-posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein-Gordon equations. Next, formal approximations of initial value problem was constructed by perturbation method and the asymptotic validity of the formal approximation is got. Finally, an application of the asymptotic theory was given, the asymptotic approximation degree of solutions for the initial value problem of a specific nonlinear Klein-Gordon equation was analyzed by using the asymptotic approximation theorem.
1 citations