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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4 citations
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TL;DR: In this paper, the application of asymptotic methods of nonlinear mechanics (the Krylov-Bogolyubov-Mitropol’skii method) and the method of separation of motions in nonlinear systems for the construction of an approximate solution of a nonlinear equation that describes a nonstationary wave process was considered.
Abstract: We consider the application of asymptotic methods of nonlinear mechanics (the Krylov-Bogolyubov-Mitropol’skii method) and the method of separation of motions in nonlinear systems for the construction of an approximate solution of a nonlinear equation that describes a nonstationary wave process.
4 citations
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TL;DR: The general fourth Painleve transcendent is studied to find a group of its asymptotics and the corresponding monodromic data, and its existence and ”uniqueness“ are proved.
Abstract: We use the uniform asymptotics method proposed by A. P. Bassom et
al. (1998) to study the general fourth Painleve transcendent, find a
group of its asymptotics and the corresponding monodromic data,
and prove its existence and ”uniqueness.“
4 citations
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TL;DR: In this paper, an integro-differential kinetic equation coupled with a Gaussian isokinetic thermostat is used for modeling complex systems in the applied sciences under the action of an external force field.
Abstract: This paper is devoted to the asymptotic analysis of a mathematical framework that has recently been proposed for modelling complex systems in the applied sciences under the action of an external force field. This framework consists in an integro-differential kinetic equation coupled with a Gaussian isokinetic thermostat. The asymptotic limit obtained here using low-field scaling shows the emergence of diffusive behaviour on a macroscopic scale.
4 citations
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TL;DR: In this paper, a three-dimensional differential system is proposed, in which the motion becomes chaotic at some parameter value, and the asymptotic solution is calculated by using Kuzmak's method.
4 citations