2007/03/07 by Jens Jonasson
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Nonlinear Waves and Solitons #Numerical methods for differential equations #math.AP #msc:35F05 #msc:35N10 #msc:58J99
paper · pdf · doi:10.1016/j.geomphys.2008.03.008
27 pages
arxiv created 2007/03/07 · openalex publication_date 2008/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
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.