Multiplication of solutions for linear overdetermined systems of partial differential equations

Details Multiplication of solutions for linear overdetermined systems of partial differential equations Multiplication of solutions for linear overdetermined systems of partial differential equations

2007-03-07

arxiv.org/abs/math/0703195v1

Mathematics

Analysis of PDEs

27 pages

Scientific paper

10.1016/j.geomphys.2008.03.008

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.

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