Thomas Decomposition of Nonlinear PDE Systems; Prof. Daniel Robertz
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This talk gives an introduction to the method of Thomas decomposition for systems of nonlinear partial differential equations, which is fundamental for solving tasks like determining all power series solutions of the PDE system (around sufficiently generic points), deciding membership of a differential equation to the corresponding radical differential ideal, determining all consequences of the system that involve only certain specified unknown functions. The algorithms have been implemented and are now available as a package in the standard distribution of Maple. Among the various applications of the method are: finding singular solutions, differential elimination, nonlinear control theory.