The nonlinear K (n;1) equation with damping is investigated via the approximate homotopy symmetry method and approximate homotopy direct method. The approximate homotopy symmetry and homotopy similarity reduction equations of different orders are derived and the corresponding homotopy series reduction solutionsare obtained. As a result, the formal coincidence for both methods is displayed.
","abstract_html":"<p>The nonlinear K (n;1) equation with damping is investigated via the approximate homotopy symmetry method and approximate homotopy direct method. The approximate homotopy symmetry and homotopy similarity reduction equations of different orders are derived and the corresponding homotopy series reduction solutionsare obtained. As a result, the formal coincidence for both methods is displayed.</p>","abstract_has_math":false,"creators":["Zhang, Rui"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Yingkang Hu","Yi Lin"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-04-01T07:00:00Z","date_published":"2013-04-01T07:00:00Z","updated_at":"2026-07-24T02:26:17Z","subjects":["ETD","Symmetry method","Direct method","Homotopy model","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/62","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Yingkang Hu","Yi Lin"]},{"key":"dc:creator","label":"Author","values":["Zhang, Rui"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-07-29T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Symmetry method","Direct method","Homotopy model","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/62"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The nonlinear K (n;1) equation with damping is investigated via the approximate homotopy symmetry method and approximate homotopy direct method. The approximate homotopy symmetry and homotopy similarity reduction equations of different orders are derived and the corresponding homotopy series reduction solutionsare obtained. As a result, the formal coincidence for both methods is displayed.
"]},{"key":"dc:title","label":"Title","values":["Approximate Similarity Reduction"]}]}],"canonical_facts":{"dc:contributor":["Yingkang Hu","Yi Lin"],"dc:creator":["Zhang, Rui"],"dc:date.available":["2013-07-29T07:00:00Z"],"dc:description.abstract":["The nonlinear K (n;1) equation with damping is investigated via the approximate homotopy symmetry method and approximate homotopy direct method. The approximate homotopy symmetry and homotopy similarity reduction equations of different orders are derived and the corresponding homotopy series reduction solutionsare obtained. As a result, the formal coincidence for both methods is displayed.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/62"],"dc:subject":["ETD","Symmetry method","Direct method","Homotopy model","Mathematics"],"dc:title":["Approximate Similarity Reduction"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:26:17Z"}