UBC Math

Thu 27 Aug 2015, 2:30pm
Symmetries and Differential Equations Seminar
Math 125

Mappings II

Math 125
Thu 27 Aug 2015, 2:30pm3:30pm
Abstract
Mappings II:
It will be shown that from the symmetries of a linear PDE system with variable coefficients, one can determine systematically whether it can be mapped invertibly to some linear PDE system with constant coefficients. We show how to find systematically such a mapping when one exists. This leads to the solution of the problem posed by Kolmogorov on when can a diffusion process be mapped into a Wiener process.
It will also be shown that from the conservation law multipliers of a nonlinear PDE system one can determine systematically whether it can be mapped invertibly to some linear PDE system. We show to find systematically such a mapping when one exists.
These results will be extended systematically to noninvertible mappings.
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