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4 papers · 2 filters
Hierarchy of Conservation Laws of Diffusion--Convection Equations
Roman O. Popovych, Nataliya M. Ivanova
We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or s…
Implementability of Liouville evolution, Koopman and Banach-Lamperti theorems in Classical and Quantum dynamics
I. Antoniou, W. A. Majewski, Z. Suchanecki
We extend the concept of implementability of semigroups of evolution operators associated with dynamical systems to quantum case. We show that such an extension can be properly for…
The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2
J. Golenia, Y. A. Prykarpatsky, A. M. Samoilenko +1
The structure properties of multidimensional Delsarte transmutation operators in parametirc functional spaces are studied by means of differential-geometric tools. It is shown that…
Potential equivalence transformations for nonlinear diffusion-convection equations
Roman O. Popovych, Nataliya M. Ivanova
Potential equivalence transformations (PETs) are effectively applied to a class of nonlinear diffusion-convection equations. For this class all possible potential symmetries are cl…