157 citations · 760 across the 31 of their papers we have counts for
17 papers · 1 filter
Symbolic computation of solitary wave solutions and solitons through homogenization of degree
Willy Hereman, Unal Goktas
A simplified version of Hirota's method for the computation of solitary waves and solitons of nonlinear PDEs is presented. A change of dependent variable transforms the PDE into an…
Lax Pairs for Edge-constrained Boussinesq Systems of Partial Difference Equations
Terry J. Bridgman, Willy Hereman
The method due to Nijhoff and Bobenko & Suris to derive Lax pairs for partial difference equations (PDeltaEs) is applied to edge constrained Boussinesq systems. These systems are d…
Symbolic Computation of Lax Pairs of Partial Difference Equations Using Consistency Around the Cube
Terry Bridgman, Willy A. Hereman, G. Reinout W. Quispel +1
A three-step method due to Nijhoff and Bobenko & Suris to derive a Lax pair for scalar partial difference equations (PΔEs) is reviewed. The method assumes that the PΔEs are defined…
Shallow Water Waves and Solitary Waves
Willy Hereman
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective;…
The Korteweg-de Vries Equation
Willy Hereman
Two page encyclopedic article about the Korteweg-de Vries equation covering historical perspective, solitary wave and periodic solutions, modern developments, properties and applic…
Scaling Invariant Lax Pairs of Nonlinear Evolution Equations
Mark Hickman, Willy Hereman, Jennifer Larue +1
A completely integrable nonlinear partial differential equation (PDE) can be associated with a system of linear PDEs in an auxiliary function whose compatibility requires that the…