Journal of Nonlinear Mathematical Physics

Volume 18, Issue Supplement 1, March 2013, 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
Corresponding Author
M. L. Gandarias
Received 30 September 2010, Accepted 2 November 2010, Available Online 7 January 2021.
DOI
https://doi.org/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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - Supplement 1
Pages
33 - 49
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S140292511100126XHow to use a DOI?
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
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  - https://doi.org/10.1142/S140292511100126X
ID  - Camacho2021
ER  -