Hokkaido Mathematical Journal

NODA Takahiro,

Equivalence problem of second order PDE for scale transformations.

Hokkaido Mathematical Journal, 40 (2011) pp.313-335

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Abstract

The purpose of the paper is to consider an equivalence problem of second order partial differential equations for one unknown function of two independent variables under scale transformations. For this equivalence problem, explicit forms of invariant functions are given. In particular, if all of these invariant functions vanish, then PDEs are equivalent to the flat equation.

MSC(Primary)58A15
MSC(Secondary)58A17
Uncontrolled Keywordssecond order partial differential equations, equivalence problem, scale transformations, G-structure