A symmetry perspective of third-order polynomial evolution equations
Date
2024
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of the Witwatersrand, Johannesburg
Abstract
In this thesis, we analyse the full class of ten Fujimoto-Watanabe equations. In particular, these are highly nonlinear third-order and two fifth-order equations. With the aid of computer algebra software such as Mathematica, we calculate symmetries for these equations and we construct their commutator tables. The
one dimensional system of optimal subalgebras is obtained via adjoint operators. Finally, we reduce these higher-order partial differential equations into ordinary differential equations, derive their solutions via a power series solution method and show how convergence may be tested. Lastly, we determine some conservation laws
Description
A thesis submitted to the Faculty of Science, University of the Witwatersrand, in requirement for the degree Doctor of Philosophy, May, 2024
Keywords
Symmetries, Polynomial evolution, UCTD
Citation
Gwaxa, Bongumusa. (2024). A symmetry perspective of third-order polynomial evolution equations [PhD thesis, University of the Witwatersrand, Johannesburg]. WireDSpace.https://hdl.handle.net/10539/41829