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ON THE CONSTRUCTION OF PARTIAL DIFFERENCE SCHEMES II: DISCRETE VARIABLES AND SCHWARZIAN LATTICES
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing a partial differential equation on an arbitrary lattice. An open problem ...
ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this ...
ON IMMERSION FORMULAS FOR SOLITON SURFACES
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
This paper is devoted to a study of the connections between three different analytic descriptions for the immersion functions of 2D-surfaces corresponding to the following three types of symmetries: gauge symmetries of the ...