Asymptotics of solutions to a second-order quasi-linear equation
type: Item
instance of: scholarly article
title: Asymptotics of solutions to a second-order quasi-linear equation
zbMATH Open document ID: 0973.34042
author: E. V. Maevskii
published in: Computational Mathematics and Mathematical Physics
publication date: 2001-11-27T00:00:00Z
review text: The author examines the asymptotic behavior of the real solution \(z(t)\) to the equation (1) \(tz''+z'+tf(z)=0\), where \(f(\xi)\) is a real function subjected to certain constraints. If \(f(\xi)=\sin{\xi}\), the equation is written as (2) \(tz''+z'+t\sin{z}=0\). This case is especially interesting since the well-known sine-Gordon equation reduces to equation (2). The asymptotics of solutions are obtained in case when \(f\) negligibly differs from sine, and the solutions satisfy initial conditions at \(t\in{\mathbb R_+}\) that are sufficiently small in absolute value.
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1472989
zbMATH Keywords: differential equation
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: second order
zbMATH Keywords: solutions
zbMATH Keywords: sine-Gordon equation
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1472989