Gwaxa, Bongumusa2023-05-082023-05-082022https://hdl.handle.net/10539/35485A dissertation submitted in fulfilment of the requirements for the degree of Master of Science to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2022In this dissertation, we apply Lie theory to determine the one-parameter point transformations which leave complex-valued Korteweg-de Vries equations in- variant. The conserved vectors of the systems are constructed. We provide travelling wave reductions that lead to third-order ordinary differential equa- tions. These equations are highly nonlinear to solve directly, and therefore we first establish their first integrals. The latter is of second-order and facilitates the solution of the complex-valued system.enDissertation