Volume 18, Issue Supplement 1, September 2011, Pages 33 - 49
Exact Travelling Wave Solutions of a Beam Equation
Authors
J. C. Camacho, M. S. Bruzón, J. Ramírez, M. L. Gandarias*
Departamento de Matemáticas, Universidad de Cádiz, P.O. Box 40, Puerto Real, Cádiz 11510, Spain
Received 30 September 2010, Accepted 2 November 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S140292511100126XHow to use a DOI?
- Keywords
- Beam equation; partial differential equation; symmetries
- Abstract
In this paper we make a full analysis of the symmetry reductions of a beam equation by using the classical Lie method of infinitesimals and the nonclassical method. We consider travelling wave reductions depending on the form of an arbitrary function. We have found several new classes of solutions that have not been considered before: solutions expressed in terms of Jacobi elliptic functions, Wadati solitons and compactons. Several classes of coherent structures are displayed by some of the solutions: kinks, solitons, two humps compactons.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - J. C. Camacho AU - M. S. Bruzón AU - J. Ramírez AU - M. L. Gandarias PY - 2021 DA - 2021/01/07 TI - Exact Travelling Wave Solutions of a Beam Equation JO - Journal of Nonlinear Mathematical Physics SP - 33 EP - 49 VL - 18 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S140292511100126X DO - 10.1142/S140292511100126X ID - Camacho2021 ER -