W
Willy Hereman
Researcher at Colorado School of Mines
Publications - 108
Citations - 4870
Willy Hereman is an academic researcher from Colorado School of Mines. The author has contributed to research in topics: Nonlinear system & Partial differential equation. The author has an hindex of 34, co-authored 107 publications receiving 4472 citations. Previous affiliations of Willy Hereman include Stellenbosch University & University of Iowa.
Papers
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The tanh method: I. Exact solutions of nonlinear evolution and wave equations
Willy Malfliet,Willy Hereman +1 more
TL;DR: In this article, a systemized version of the tanh method is used to solve particular evolution and wave equations, where the boundary conditions are implemented in this expansion, and the associated velocity can then be determined a priori, provided the solution vanishes at infinity.
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Symbolic methods to construct exact solutions of nonlinear partial differential equations
Willy Hereman,Ameina S. Nuseir +1 more
TL;DR: In this paper, a simplified version of Hirota's method is used to find closed-form soliton solutions of the Fitzhugh-Nagumo equation with convection term and an evolution equation due to Calogero.
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The tanh method: II. Perturbation technique for conservative systems
Willy Malfliet,Willy Hereman +1 more
TL;DR: In this paper, a general wave profile, with a perturbative solitary-wave contribution superposed, was obtained for a particular choice of the parameters, and a comparison with the exact solution was made.
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Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method
Willy Hereman,Partha P. Banerjee,Adrianus Korpel,Gaetano Assanto,A. Van Immerzeele,A. Meerpoel +5 more
TL;DR: In this paper, the authors present a systematic and formal approach toward finding solitary wave solutions of nonlinear evolution and wave equations from the real exponential solutions of the underlying linear equations, where the physical concept is one of the mixing of these elementary solutions through the nonlinearities in the system.
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Symbolic Computation of Conserved Densities for Systems of Nonlinear Evolution Equations
Unal Goktas,Willy Hereman +1 more
TL;DR: A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented and the code is tested on several well-known partial differential equations from soliton theory.