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Title:Stability of periodic solutions to nonlinear Klein-Gordon equations
Author(s):Venkatasubbu, Nanjundamurthy
Advisor(s):Bronski, Jared C.
Department / Program:Aerospace Engineering
Discipline:Aerospace Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):nonlinear klein gordon equation
modulational instability
periodic solutions
evans function
stability index
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)
Issue Date:2012-12
Rights Information:Copyright 2012 by Nanjundamurthy Venkatasubbu. All rights reserved.
Date Available in IDEALS:2013-02-03
Date Deposited:2012-12

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