A symmetry perspective of third-order polynomial evolution equations

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