Gwaxa, Bongumusa2024-10-232024-10-232024Gwaxa, Bongumusa. (2024). A symmetry perspective of third-order polynomial evolution equations [PhD thesis, University of the Witwatersrand, Johannesburg]. WireDSpace.https://hdl.handle.net/10539/41829https://hdl.handle.net/10539/41829A thesis submitted to the Faculty of Science, University of the Witwatersrand, in requirement for the degree Doctor of Philosophy, May, 2024In 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 lawsen© 2024 University of the Witwatersrand, Johannesburg. All rights reserved. The copyright in this work vests in the University of the Witwatersrand, Johannesburg. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of University of the Witwatersrand, Johannesburg.SymmetriesPolynomial evolutionUCTDSDG-17: Partnerships for the goalsThesisUniversity of the Witwatersrand, Johannesburg