{"id":{"repo_id":"sask","oai_identifier":"oai:harvest.usask.ca:10388/etd-05312011-142943"},"canonical_url":"https://search.dev.ndltd.org/etd/sask/oai:harvest.usask.ca:10388/etd-05312011-142943","repository":{"repo_id":"sask","name":"University of Saskatchewan","base_url":"https://harvest.usask.ca/server/oai/request"},"display":{"title":"Symbolic software for symmetry reduction and computation of invariant solutions of differential equations","abstract":"Problems involving partial or ordinary differential equations arise in various fields of science. Therefore, the task of obtaining exact solutions of differential equations is of primary importance, and attracts high attention. The main purpose of the current thesis is the development of a Maple-based, symbolic software package for symmetry reduction of differential equations and computation of symmetry-invariant solutions. The package developed in the current thesis is compatible with and can be viewed as an extension of the package GeM for symbolic symmetry analysis, developed by Prof. Alexei Cheviakov. The reduction procedure is based on the Lie's classical symmetry reduction method involving canonical coordinates. The developed package is applicable for obtaining solutions arising from extension of Lie's method, in particular, nonlocal and approximate symmetries. The developed software is applied to a number of PDE problems to obtain exact invariant solutions. The considered equations include the one-dimensional nonlinear heat equation, the potential Burgers' equation, as well as equations arising in nonlinear elastostatics and elastodynamics.","abstract_html":"Problems involving partial or ordinary differential equations arise in various fields of science. Therefore, the task of obtaining exact solutions of differential equations is of primary importance, and attracts high attention. The main purpose of the current thesis is the development of a Maple-based, symbolic software package for symmetry reduction of differential equations and computation of symmetry-invariant solutions. The package developed in the current thesis is compatible with and can be viewed as an extension of the package GeM for symbolic symmetry analysis, developed by Prof. Alexei Cheviakov. The reduction procedure is based on the Lie's classical symmetry reduction method involving canonical coordinates. The developed package is applicable for obtaining solutions arising from extension of Lie's method, in particular, nonlocal and approximate symmetries. The developed software is applied to a number of PDE problems to obtain exact invariant solutions. The considered equations include the one-dimensional nonlinear heat equation, the potential Burgers' equation, as well as equations arising in nonlinear elastostatics and elastodynamics.","abstract_has_math":false,"creators":["Olinov, Andrey I."],"institution":"University of Saskatchewan","degree_name":"Master of Science (M.Sc.)","degree_level":"Masters","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":[],"advisors":["Cheviakov, Alexei F."],"committee_chairs":[],"committee_members":["Bikis, Miķelis G.","Szmigielski, Jacek","Koustov, Sasha"],"year":2011,"date_issued":"2011-05","date_published":"2011-05","updated_at":"2026-07-24T04:27:16Z","subjects":["Invariant solutions","Symmetry reduction"],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10388/etd-05312011-142943","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Cheviakov, Alexei F."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Bikis, Miķelis G.","Szmigielski, Jacek","Koustov, Sasha"]},{"key":"dc:creator","label":"Author","values":["Olinov, Andrey I."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2011-05-31T14:29:43Z","2013-01-04T04:34:28Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2012-06-24T08:00:00Z","2013-01-04T04:34:28Z"]},{"key":"dc:date.issued","label":"Date","values":["2011-05"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (M.Sc.)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Saskatchewan"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Invariant solutions","Symmetry reduction"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10388/etd-05312011-142943"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Problems involving partial or ordinary differential equations arise in various fields of science. Therefore, the task of obtaining exact solutions of differential equations is of primary importance, and attracts high attention. The main purpose of the current thesis is the development of a Maple-based, symbolic software package for symmetry reduction of differential equations and computation of symmetry-invariant solutions. The package developed in the current thesis is compatible with and can be viewed as an extension of the package GeM for symbolic symmetry analysis, developed by Prof. Alexei Cheviakov. The reduction procedure is based on the Lie's classical symmetry reduction method involving canonical coordinates. The developed package is applicable for obtaining solutions arising from extension of Lie's method, in particular, nonlocal and approximate symmetries. The developed software is applied to a number of PDE problems to obtain exact invariant solutions. The considered equations include the one-dimensional nonlinear heat equation, the potential Burgers' equation, as well as equations arising in nonlinear elastostatics and elastodynamics."]},{"key":"dc:title","label":"Title","values":["Symbolic software for symmetry reduction and computation of invariant solutions of differential equations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Cheviakov, Alexei F."],"dc:contributor.committeemember":["Bikis, Miķelis G.","Szmigielski, Jacek","Koustov, Sasha"],"dc:creator":["Olinov, Andrey I."],"dc:date.accessioned":["2011-05-31T14:29:43Z","2013-01-04T04:34:28Z"],"dc:date.available":["2012-06-24T08:00:00Z","2013-01-04T04:34:28Z"],"dc:date.issued":["2011-05"],"dc:description.abstract":["Problems involving partial or ordinary differential equations arise in various fields of science. Therefore, the task of obtaining exact solutions of differential equations is of primary importance, and attracts high attention. The main purpose of the current thesis is the development of a Maple-based, symbolic software package for symmetry reduction of differential equations and computation of symmetry-invariant solutions. The package developed in the current thesis is compatible with and can be viewed as an extension of the package GeM for symbolic symmetry analysis, developed by Prof. Alexei Cheviakov. The reduction procedure is based on the Lie's classical symmetry reduction method involving canonical coordinates. The developed package is applicable for obtaining solutions arising from extension of Lie's method, in particular, nonlocal and approximate symmetries. The developed software is applied to a number of PDE problems to obtain exact invariant solutions. The considered equations include the one-dimensional nonlinear heat equation, the potential Burgers' equation, as well as equations arising in nonlinear elastostatics and elastodynamics."],"dc:identifier.uri":["https://hdl.handle.net/10388/etd-05312011-142943"],"dc:language.iso":["en_US"],"dc:subject":["Invariant solutions","Symmetry reduction"],"dc:title":["Symbolic software for symmetry reduction and computation of invariant solutions of differential equations"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Masters"],"thesis:degree_name":["Master of Science (M.Sc.)"],"thesis:institution_name":["University of Saskatchewan"]},"updated_at":"2026-07-24T04:27:16Z"}