157 citations · 760 across the 31 of their papers we have counts for
32 papers
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…
Collisions of acoustic solitons and their electric fields in plasmas at critical compositions
Frank Verheest, Willy A. Hereman
Acoustic solitons obtained through a reductive perturbation scheme are normally governed by a Korteweg-de Vries (KdV) equation. In multispecies plasmas at critical compositions the…
Traveling Wave Solutions to Fifth- and Seventh-order Korteweg-de Vries Equations: Sech and Cn Solutions
Stefan C. Mancas, Willy A. Hereman
In this paper we review the physical relevance of a Korteweg-de Vries (KdV) equation with higher-order dispersion terms which is used in the applied sciences and engineering. We al…
Modified Korteweg-de Vries solitons at supercritical densities in two-electron temperature plasmas
Frank Verheest, Carel P. Olivier, Willy A. Hereman
The supercritical composition of a plasma model with cold positive ions in the presence of a two-temperature electron population is investigated, initially by a reductive perturbat…
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…