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Bronski, Jared C. Venkatasubbu, Nanjundamurthy 2013-02-03T19:28:19Z 2013-02-03T19:28:19Z 2012-12 2012-12 2012-12 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then verified for the following cases: • cubic nonlinearity; F(u) = u3 − u • sine Gordon equation; F(u) = − sin(u) Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-12-13T14:57:46Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 Venkatasubbu_Nanjundamurthy.pdf: 391388 bytes, checksum: 461c9daedc5b39c0eaf625b23a98d8c3 (MD5) Venkatasubbu_Nanjundamurthy.pdf: 391388 bytes, checksum: 461c9daedc5b39c0eaf625b23a98d8c3 (MD5) Made available in DSpace on 2013-02-03T19:28:19Z (GMT). No. of bitstreams: 2 Nanjundamurthy_Venkatasubbu.pdf: 391388 bytes, checksum: 461c9daedc5b39c0eaf625b23a98d8c3 (MD5) license.txt: 4077 bytes, checksum: be1bc3f259ac54c4eee161aab4b49add (MD5) http://hdl.handle.net/2142/42221 en Copyright 2012 by Nanjundamurthy Venkatasubbu. All rights reserved. nonlinear klein gordon equation modulational instability periodic solutions evans function stability index Stability of periodic solutions to nonlinear Klein-Gordon equations text Aerospace Engineering 1615 Aerospace Engineering 4048 University of Illinois at Urbana-Champaign Thesis M.S. MS: Aerospace Engr -UIUC 10KS4048MS