{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/42221"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/42221","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stability of periodic solutions to nonlinear Klein-Gordon equations","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)","abstract_html":"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_has_math":false,"creators":["Venkatasubbu, Nanjundamurthy"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":["Bronski, Jared C."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-02-03T19:28:19Z","date_published":"2013-02-03T19:28:19Z","updated_at":"2026-07-22T22:25:33Z","subjects":["nonlinear klein gordon equation","modulational instability","periodic solutions","evans function","stability index"],"languages":["en"],"rights":["Copyright 2012 by Nanjundamurthy Venkatasubbu. All rights reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/42221","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bronski, Jared C."]},{"key":"dc:creator","label":"Author","values":["Venkatasubbu, Nanjundamurthy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-02-03T19:28:19Z","2012-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["nonlinear klein gordon equation","modulational instability","periodic solutions","evans function","stability index"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2012 by Nanjundamurthy Venkatasubbu. 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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). 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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). 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