Article ID Journal Published Year Pages File Type
1898849 Journal of Geometry and Physics 2008 15 Pages PDF
Abstract

A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE’s contains the Cauchy–Riemann equations and the cofactor pair systems, included as special cases. The multiplication provides a method for generating, in a pure algebraic way, large classes of non-trivial solutions that can be constructed by forming convergent power series of trivial solutions.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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