157 citations · 760 across the 31 of their papers we have counts for
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Continuous and Discrete Homotopy Operators: A Theoretical Approach made Concrete
W. Hereman, B. Deconinck, L. D. Poole
Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those i…
Symbolic Computation of Conservation Laws of Nonlinear Partial Differential Equations in Multi-dimensions
Willy Hereman
A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The m…
Symbolic Software for the Painleve Test of Nonlinear Ordinary and Partial Differential Equations
Douglas Baldwin, Willy Hereman
The automation of the traditional Painleve test in Mathematica is discussed. The package PainleveTest.m allows for the testing of polynomial systems of ordinary and partial differe…
Continuous and Discrete Homotopy Operators with Applications in Integrability Testing
Willy Hereman, Michael Colagrosso, Ryan Sayers +4
We introduce calculus-based formulas for the continuous Euler and homotopy operators. The 1D continuous homotopy operator automates integration by parts on the jet space. Its 3D ge…