The complex-valued class of Korteweg-de Vries equations

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2022

Authors

Gwaxa, Bongumusa

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Abstract

In 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.

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A 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, 2022

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