SYMMETRIES OF PARTIAL DIFFERENTIAL EQUATIONS
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We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations.
completely integrable systems, Mathematics - Differential Geometry, Mathematics - Complex Variables, Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables, Extension of functions and other analytic objects from CR manifolds, CR functions, Primary: 32V40, 34C14. Secondary 32V25, 32H02, 32H40, 32V10, Real submanifolds in complex manifolds, generic CR submanifolds, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG], Symmetries, invariants of ordinary differential equations, Boundary regularity of mappings in several complex variables
completely integrable systems, Mathematics - Differential Geometry, Mathematics - Complex Variables, Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables, Extension of functions and other analytic objects from CR manifolds, CR functions, Primary: 32V40, 34C14. Secondary 32V25, 32H02, 32H40, 32V10, Real submanifolds in complex manifolds, generic CR submanifolds, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG], Symmetries, invariants of ordinary differential equations, Boundary regularity of mappings in several complex variables
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