Zobrazeno 1 - 10
of 133
pro vyhledávání: '"Hereman, Willy A."'
Autor:
Naz, Rehana, Hereman, Willy
The Lie-point symmetry method is used to find some closed-form solutions for a constitutive equation modeling stress in elastic materials. The partial differential equation (PDE), which involves a power law with arbitrary exponent n, was investigated
Externí odkaz:
http://arxiv.org/abs/2409.15593
Autor:
Hereman, Willy, Göktaş, Ünal
Publikováno v:
Mathematical and Computational Applications 29(5), 91, 35pp (2024)
Using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations thereby establishing their complete i
Externí odkaz:
http://arxiv.org/abs/2408.07973
Autor:
Hereman, Willy, Goktas, Unal
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 equation that is homogeneous of degree. Solitons are then computed us
Externí odkaz:
http://arxiv.org/abs/2307.08888
Autor:
Bridgman, Terry J., Hereman, Willy
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 defined on a quadrilateral. They are consistent around the cube but the
Externí odkaz:
http://arxiv.org/abs/1909.10738
Autor:
Verheest, Frank, Hereman, Willy A.
Publikováno v:
Journal of Plasma Physics, Vol. 85, Issue 1, Art. No. 905850106, 2019
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 coefficient of the quadratic nonlinearity vanishes. Extending the ana
Externí odkaz:
http://arxiv.org/abs/1901.06472
Autor:
Mancas, Stefan C., Hereman, Willy A.
Publikováno v:
J. Phys. Soc. Jpn. 87, 114002 (2018) [8 Pages]
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 also present exact traveling wave solutions to this generalized KdV equa
Externí odkaz:
http://arxiv.org/abs/1809.03494
Publikováno v:
Journal of Plasma Physics, vol. 82, Art. No. 905820208, 13 pages (2016)
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 perturbation approach, under the combined requirements that there be neither qu
Externí odkaz:
http://arxiv.org/abs/1604.03097
Publikováno v:
Foundations of Computational Mathematics, 13(4), 517-544 (2013)
A three-step method due to Nijhoff and Bobenko & Suris to derive a Lax pair for scalar partial difference equations (P\Delta Es) is reviewed. The method assumes that the P\Delta Es are defined on a quadrilateral, and consistent around the cube. Next,
Externí odkaz:
http://arxiv.org/abs/1308.5473
Autor:
Hereman, Willy
Publikováno v:
Original article was published in the Encyclopedia of Complexity and Applied System Science, ed. Robert A. Meyers, Entry 480, pp. 8112-8125, Springer-Verlag, Heidelberg, 2009, ISBN 978-0-387-75888-6
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow Water Wave
Externí odkaz:
http://arxiv.org/abs/1308.5383
Autor:
Hereman, Willy
Two page encyclopedic article about the Korteweg-de Vries equation covering historical perspective, solitary wave and periodic solutions, modern developments, properties and applications, and further reading.
Comment: To appear in The Princeton
Comment: To appear in The Princeton
Externí odkaz:
http://arxiv.org/abs/1308.5306