Show simple item record

dc.contributor.advisorGomes, Diogo A.
dc.contributor.authorAlghamdi, Moataz
dc.date.accessioned2017-06-18T10:59:06Z
dc.date.available2017-06-18T10:59:06Z
dc.date.issued2017-06-18
dc.identifier.citationAlghamdi, M. (2017). Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations. KAUST Research Repository. https://doi.org/10.25781/KAUST-9LI3T
dc.identifier.doi10.25781/KAUST-9LI3T
dc.identifier.urihttp://hdl.handle.net/10754/625045
dc.description.abstractWe introduce a symbolic computational approach to detecting all permutation and parity symmetries in any general evolution equation, and to generating associated invariant polynomials, from given monomials, under the action of these symmetries. Traditionally, discrete point symmetries of differential equations are systemically found by solving complicated nonlinear systems of partial differential equations; in the presence of Lie symmetries, the process can be simplified further. Here, we show how to find parity- and permutation-type discrete symmetries purely based on algebraic calculations. Furthermore, we show that such symmetries always form groups, thereby allowing for the generation of new group-invariant conserved quantities from known conserved quantities. This work also contains an implementation of the said results in Mathematica. In addition, it includes, as a motivation for this work, an investigation of the connection between variational symmetries, described by local Lie groups, and conserved quantities in Hamiltonian systems.
dc.language.isoen
dc.subjectsymmetry
dc.subjectpermutation
dc.subjectevolution
dc.subjectpurity
dc.titleSymbolic Detection of Permutation and Parity Symmetries of Evolution Equations
dc.typeThesis
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberTempone, Raul
dc.contributor.committeememberSun, Shuyu
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameMaster of Science
refterms.dateFOA2018-06-13T14:20:04Z


Files in this item

Thumbnail
Name:
Thesis_MoatazAlghamdi.pdf
Size:
310.8Kb
Format:
PDF

This item appears in the following Collection(s)

Show simple item record