A model with nonlinear Schrödinger (NLS) equation used for describing pulse propagations in photopolymers is considered. We focus on a case in which change of refractive index is proportional to the square of amplitude of the electric field and consider 2-dimensional spatial domain. After formal derivation of the NLS approximation from the wave-Maxwell equation, we establish well-posedness and perform rigorous justification analysis to show smallness of error terms for appropriately small time intervals. We conclude by numerical simulation to illustrate the results in one-dimensional case.
","abstract_html":"<p>A model with nonlinear Schrödinger (NLS) equation used for describing pulse propagations in photopolymers is considered. We focus on a case in which change of refractive index is proportional to the square of amplitude of the electric field and consider 2-dimensional spatial domain. After formal derivation of the NLS approximation from the wave-Maxwell equation, we establish well-posedness and perform rigorous justification analysis to show smallness of error terms for appropriately small time intervals. We conclude by numerical simulation to illustrate the results in one-dimensional case.</p>","abstract_has_math":false,"creators":["Ponomarev, Dmitry"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Mathematics and Statistics","school":null,"contributors":[],"advisors":["Pelinovsky, Dmitry"],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-10","date_published":"2012-10","updated_at":"2026-08-21T16:46:33Z","subjects":["justification analysis","photopolymers","NLS equation","wave-Maxwell system","Optics","Partial Differential Equations","Polymer Chemistry"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["opendissertations/6981","8018","2843310"],"render_values":[{"text":"opendissertations/6981","href":null,"code":true},{"text":"8018","href":null,"code":true},{"text":"2843310","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/11375/12064","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://macsphere.mcmaster.ca/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Amacsphere.mcmaster.ca%3A11375%2F12064","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Pelinovsky, Dmitry"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics and Statistics"]},{"key":"dc:creator","label":"Author","values":["Ponomarev, Dmitry"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-06-18T16:58:08Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-06-18T16:58:08Z"]},{"key":"dc:date.issued","label":"Date","values":["2012-10"]},{"key":"dc:type","label":"Dc Type","values":["thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["justification analysis","photopolymers","NLS equation","wave-Maxwell system","Optics","Partial Differential Equations","Polymer Chemistry"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["opendissertations/6981","8018","2843310"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11375/12064"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A model with nonlinear Schrödinger (NLS) equation used for describing pulse propagations in photopolymers is considered. We focus on a case in which change of refractive index is proportional to the square of amplitude of the electric field and consider 2-dimensional spatial domain. After formal derivation of the NLS approximation from the wave-Maxwell equation, we establish well-posedness and perform rigorous justification analysis to show smallness of error terms for appropriately small time intervals. We conclude by numerical simulation to illustrate the results in one-dimensional case.
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