Generalized symmetry and reductions of nonlinear partial differential equations
dr hab. Ivan Tsyfra, AGH, Wydział Matematyki Stosowanej
Chair of Mathematical Physics, 2025-06-13 godz. 9:45 - 11:15
The method of conditional (nonclassical) symmetry, which is a generalization of the classical one, is presented. Exact solutions of nonlinear wave and heat equations are obtained with the help of this method. These solutions cannot be obtained within the framework of the classical Lie approach. The method is extended to non-point symmetry operators. Using the nonlinear wave equation as an example, it is shown that conditional symmetry operators can be used to construct the Lie–Bäcklund transformations. We also apply the inverse symmetry reduction method to reduce and find solutions of the nonlinear 4-dimensional Plebanski equation (the second heavenly equation).
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