Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations

Handle URI:
http://hdl.handle.net/10754/625045
Title:
Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations
Authors:
Alghamdi, Moataz ( 0000-0001-9640-8438 )
Abstract:
We 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.
Advisors:
Gomes, Diogo A. ( 0000-0002-3129-3956 )
Committee Member:
Tempone, Raul ( 0000-0003-1967-4446 ) ; Sun, Shuyu ( 0000-0002-3078-864X )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
18-Jun-2017
Type:
Thesis
Appears in Collections:
Theses

Full metadata record

DC FieldValue Language
dc.contributor.advisorGomes, Diogo A.en
dc.contributor.authorAlghamdi, Moatazen
dc.date.accessioned2017-06-18T10:59:06Z-
dc.date.available2017-06-18T10:59:06Z-
dc.date.issued2017-06-18-
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.en
dc.language.isoenen
dc.subjectsymmetryen
dc.subjectpermutationen
dc.subjectevolutionen
dc.subjectpurityen
dc.titleSymbolic Detection of Permutation and Parity Symmetries of Evolution Equationsen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberTempone, Raulen
dc.contributor.committeememberSun, Shuyuen
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id142754en
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