{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/79980"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/79980","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"Small Dispersion Limits for Integrable Nonlinear Wave Equations with Periodic Initial Conditions","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Deng, Guo"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Biondini, Gino","Physics"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-07-30T15:11:35Z","date_published":"2019-07-30T15:11:35Z","updated_at":"2026-07-27T19:05:21Z","subjects":["applied mathematics"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/79980","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Biondini, Gino","Physics"]},{"key":"dc:creator","label":"Author","values":["Deng, Guo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-07-30T15:11:35Z","2019","2019-05-16 12:21:04"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["applied mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/79980"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","Partial differential equations (PDEs) has been an active research branch since the eighteenth century. Initially research interests in this field were mainly focused on Laplace's equation, the heat equation and the wave equation, all of which are linear PD Es. However, the real-world models are usually nonlinear, therefore more and more works have been devoted to nonlinear PDEs in recent years. As ubiquitous phenomena, nonlinear waves, which are governed by nonlinear evolution PDEs, have attracted many research interests. Among these nonlinear PDEs describing wave phenomena, the Korteweg-deVries (KdV) equation and the nonlinear Schrodinger (NLS) equation are important from both a physical and a mathematical point of view. Because of their universal character, these equations arise as fundamental models in various physical areas. The KdV equation was first introduced by Boussinesq (1877) [13] and rediscovered by Diederik Korteweg and Gustav de Vries (1895) [51] to describe the evolution of water waves in shallow water. In the 20th century, it was also derived as a model in plasma physics, cosmology and other physical settings [18]. The NLS equation was derived in the 1960's as a governing equation for water waves [99]. It also arises in the field of light propagation through optical fibers [5], plasma physics [37] and Bose-Einstein condensates [14], and is in fact a universal model for the evolution of weakly nonlinear dispersive wave trains. Mathematically, each of these equations is a completely integrable Hamiltonian system, which is equivalent to the compatibility condition of certain overdetermined linear system of differential equations, also known as Lax pair. By exploiting the associated Lax pair, these equations can be solved in explicit ways via the inverse scattering transform (IST) [4 , 8, 32 , 48 , 58 , 66], which is a nonlinear analogue of the Fourier transform for linear PDEs. Because these equation possess a rich mathematical structure, they have been cutting-edge research topics for decades, and continue to offer challenging research opportunities.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Small Dispersion Limits for Integrable Nonlinear Wave Equations with Periodic Initial Conditions"]}]}],"canonical_facts":{"dc:contributor":["Biondini, Gino","Physics"],"dc:creator":["Deng, Guo"],"dc:date":["2019-07-30T15:11:35Z","2019","2019-05-16 12:21:04"],"dc:description":["Ph.D.","Partial differential equations (PDEs) has been an active research branch since the eighteenth century. Initially research interests in this field were mainly focused on Laplace's equation, the heat equation and the wave equation, all of which are linear PD Es. However, the real-world models are usually nonlinear, therefore more and more works have been devoted to nonlinear PDEs in recent years. As ubiquitous phenomena, nonlinear waves, which are governed by nonlinear evolution PDEs, have attracted many research interests. Among these nonlinear PDEs describing wave phenomena, the Korteweg-deVries (KdV) equation and the nonlinear Schrodinger (NLS) equation are important from both a physical and a mathematical point of view. Because of their universal character, these equations arise as fundamental models in various physical areas. The KdV equation was first introduced by Boussinesq (1877) [13] and rediscovered by Diederik Korteweg and Gustav de Vries (1895) [51] to describe the evolution of water waves in shallow water. In the 20th century, it was also derived as a model in plasma physics, cosmology and other physical settings [18]. The NLS equation was derived in the 1960's as a governing equation for water waves [99]. It also arises in the field of light propagation through optical fibers [5], plasma physics [37] and Bose-Einstein condensates [14], and is in fact a universal model for the evolution of weakly nonlinear dispersive wave trains. Mathematically, each of these equations is a completely integrable Hamiltonian system, which is equivalent to the compatibility condition of certain overdetermined linear system of differential equations, also known as Lax pair. By exploiting the associated Lax pair, these equations can be solved in explicit ways via the inverse scattering transform (IST) [4 , 8, 32 , 48 , 58 , 66], which is a nonlinear analogue of the Fourier transform for linear PDEs. Because these equation possess a rich mathematical structure, they have been cutting-edge research topics for decades, and continue to offer challenging research opportunities.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/79980"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["applied mathematics"],"dc:title":["Small Dispersion Limits for Integrable Nonlinear Wave Equations with Periodic Initial Conditions"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:21Z"}