I've been using Mathematica since February of 1994. Over the years, I have become an expert at writing efficent and elegant Mathematica code. For a quick introduction to Mathematica, see my short Mathematica tutorial (PDF).
Our Painlevé test software, PainleveTest.m, performs the standard Painlevé test on systems of nonlinear polynomial ordinary and partial differential equations (ODEs and PDEs). For more information, see our paper Symbolic software for the Painlevé test of nonlinear ordinary and partial differential equations.
Our software searches for solitary wave solutions expressible in hyperbolic and elliptic functions.
The software, PDESpecialSolutions.m, allows for the computation of solutions expressible in hyperbolic tangent, hyperbolic secant, and Jacobi ellitpic functions. For more information, see our paper Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs.
The software, DDESpecialSolutions.m, allows for the computation of solutions expressible in hyperbolic tangent functions. For more information, see our paper Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations.
The software, PDERecursionOperator.m, generates a candidate recursion operator and tests it using the defining equation (Lie derivative). For more information, see our paper Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs.