Stability of periodic solutions to nonlinear Klein-Gordon equations
type: CreativeWork
description: We study the stability of periodic travelling wave solutions to nonlinear Klein-Gordon equations, subject to small and localized perturbations. Using the periodic Evans function technique, we analyze the spectrum of a linearized quadratic eigenvalue pencil associated with the linearized equation, in a neighbourhood of the origin on the spectral plane. The stability criterion is expressed in terms of signature of an index involving physical parameters of the wave, thereby holding the result valid for a general nonlinearity F(u). The result is then verified for the following cases: • cubic nonlinearity; F(u) = u3 − u • sine Gordon equation; F(u) = − sin(u)
abstract: We study the stability of periodic travelling wave solutions to nonlinear Klein-Gordon equations, subject to small and localized perturbations. Using the periodic Evans function technique, we analyze the spectrum of a linearized quadratic eigenvalue pencil associated with the linearized equation, in a neighbourhood of the origin on the spectral plane. The stability criterion is expressed in terms of signature of an index involving physical parameters of the wave, thereby holding the result valid for a general nonlinearity F(u). The result is then verified for the following cases: • cubic nonlinearity; F(u) = u3 − u • sine Gordon equation; F(u) = − sin(u)
author: Venkatasubbu, Nanjundamurthy
language: en
keywords: nonlinear klein gordon equation, modulational instability, periodic solutions, evans function, stability index
date published: 2013-02-03T19:28:19Z
date modified: 2026-07-22T22:25:33Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/42221