Stability of periodic solutions to nonlinear Klein-Gordon equations

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)

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Aerospace Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Venkatasubbu, Nanjundamurthy

Contributors dc:contributor

• Bronski, Jared C.

• nonlinear klein gordon equation
• modulational instability
• periodic solutions
• evans function
• stability index

Statement dc:rights

• Copyright 2012 by Nanjundamurthy Venkatasubbu. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/42221

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/42221