Multiplication of solutions for linear overdetermined systems of partial differential equations
arXiv:math/0703195 · doi:10.1016/j.geomphys.2008.03.008
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.
27 pages