In this contribution, we determine the exact solutions of the potential Kortewegde Vries equation, a partial differential equation (PDE). The procedure followed involves first transforming this equation into an ordinary differential equation (ODE), using Sophus Lie' symmetry group theoretical methods. The resulting ODE is then resolved through a procedure developed through differentiable topological methods, a technique developed by the third author. The pure Lie approach leads to un-integrable integrals.
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