Show simple item record

FieldValueLanguage
dc.contributor.authorAlrashdi, Huda Daefallh A
dc.date.accessioned2019-11-04
dc.date.available2019-11-04
dc.date.issued2019-06-18
dc.identifier.urihttps://hdl.handle.net/2123/21311
dc.description.abstractThe main objective of this thesis is to derive hierarchies of q-discrete Painelevé equations. Some of the important properties of these hierarchies will also be given, namely Lax pairs, Bäcklund transformations, solutions of their associated linear problems for special values of parameters and their symmetry groups. To construct these hierarchies, we apply a geometric reduction and a staircase method on a multi-parameteric generalized lattice modified Korteweg-de Vries equation. In addition, the property of consistency around the cube is used in order to find Bäcklund transformations. Starting with the base case of q-discrete second, third and fourth Painlevé equations on A_5 initial-values surface, new hierarchies of q-discrete third and fourth Painlevé equations are discovered, and we also rediscover the hierarchy of q-discrete second Painlevé equation. In this thesis, we provide the Lax pairs for each member in these hierarchies. Using the consistency around the cube, we also provide Bäcklund transformation for the entire hierarchy of q-discrete second and third Painlevé hierarchies. We generate a hierarchy of special solutions starting with seed solutions for q-discrete second and third Painlevé hierarchies. An assumption made is that particular parameter values would enable the ability to diagonalize the Lax pair. As a consequence, we found that the associated linear problem for the three hierarchies can be solved in terms of q-Gamma function. Furthermore, the hierarchy of q-discrete fourth Painlevé hierarchy can be reduced to one equation that can be linearlized to become Riccati equation which has hypergeometric special solutions. Finally, we investigated the affine Weyl group structure of the symmetry group for each hierarchy. In this thesis, we construct the explicit representation of the symmetry group for the first and second member of these hierarchies.en_AU
dc.publisherUniversity of Sydneyen_AU
dc.publisherFaculty of Scienceen_AU
dc.publisherSchool of Mathematics and Statisticsen_AU
dc.rightsThe author retains copyright of this thesis. It may only be used for the purposes of research and study. It must not be used for any other purposes and may not be transmitted or shared with others without prior permission.en_AU
dc.subjectq-discrete Painleve equationsen_AU
dc.subjectHierarchyen_AU
dc.subjectBäcklund transformationen_AU
dc.subjectLax Pairsen_AU
dc.subjectSymmetry groupen_AU
dc.titleq-discrete Painleve equations, their hierarchies and propertiesen_AU
dc.typePhD Doctorateen_AU
dc.type.pubtypeDoctor of Philosophy Ph.D.en_AU
dc.description.disclaimerAccess is restricted to staff and students of the University of Sydney . UniKey credentials are required. Non university access may be obtained by visiting the University of Sydney Library.en_AU


Show simple item record

Associated file/s

Associated collections

Share

Share:

Show simple item record

There are no previous versions of the item available.