Symbolic and numeric computation of symmetries for a class of Schrödinger Equations

An important and challenging computational problem is to identify and include the missing compatibility (integrability) conditions for general systems of partial differential equations. The inclusion of such missing conditions is executed by the application of differential-elimination algorithms. Differential equations arising during modeling generally contain both exactly known coefficients and coefficients known approximately from data. We focus on our recent work on approximate differential-elimination methods and in particular their application to the determination of approximate symmetries. We illustrate this with applications to a class of Schrödinger equations.