| Abstract: |
| Invariants of symmetry groups under transformations of dependent and independent variables lead to simplification of differential equations and their exact solutions if solutions of the transformed equations are known. Though Lie had developed his Symmetry Analysis for complex functions of complex variables, he did not explicitly use complex analyticity. We developed Complex Symmetry Analysis in which we make explicit use of the Cauchy-Riemann equations and find that one can solve systems of differential equations by it for equations not readily amenable to the usual real methods. We show that, via complex methods, one can deduce invariants that are not readily obtainable by real methods |
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