Christodoulos Sophocleous

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This paper completes investigation of symmetry properties of nonlinear variable coefficient diffusion–convection equations of the form f(x)ut = (g(x)A(u)ux)x+h(x)B(u)ux which was started in [9–11]. Potential symmetries of equations from the considered class are found and the connection of them with Lie symmetries of diffusion-type equations is shown. Exact(More)
Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivska Str., Kyiv-4, 01601 Ukraine Department of Mathematics, Eastern University, Chenkalady, Sri Lanka ♮Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, A-1090 Wien, Austria Department of Mathematics and Statistics, University of Cyprus, Nicosia CY 1678, Cyprus vaneeva@imath.kiev.ua,(More)
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding potential symmetries for the systems with multidimensional spaces of conservation laws. A class of variable coefficient(More)
We prove that the classical, non–periodic Toda lattice is super–integrable. In other words, we show that it possesses 2N−1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient of the proof is the use of some special action–angle coordinates introduced by Moser to solve the equations of motion. Mathematics Subject(More)
We consider the one-dimensional porous medium equation ut = (u nux)x+ μ x uux. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some cases this porous medium equation is connected with well known equations. With the introduction of a new dependent variable this partial(More)