On the elliptical solutions of models connected to the short pulse equation
Volume 30, Issue 4, pp 381--389
http://dx.doi.org/10.22436/jmcs.030.04.07
Publication Date: February 18, 2023
Submission Date: November 09, 2022
Revision Date: January 15, 2023
Accteptance Date: January 30, 2023
Authors
S. Jamal
- School of Mathematics, University of the Witwatersrand, Johannesburg, Wits 2001, South Africa.
R. Champala
- School of Mathematics, University of the Witwatersrand, Johannesburg, Wits 2001, South Africa.
Abstract
In the present paper, we
consider a special hierarchy of equations comprising the short pulse equation, the sine-Gordon integrable hierarchy and the elastic beam equation. These equations are highly non-linear and rely on transformations to arrive at solutions. Previously, recursion operators and hodograph mappings were successful in reducing these equations. However, we show that via the
conservation laws or the one-parameter Lie group, the special hierarchy may be integrated and will admit the exact solutions that feature elliptical functions.
Share and Cite
ISRP Style
S. Jamal, R. Champala, On the elliptical solutions of models connected to the short pulse equation, Journal of Mathematics and Computer Science, 30 (2023), no. 4, 381--389
AMA Style
Jamal S., Champala R., On the elliptical solutions of models connected to the short pulse equation. J Math Comput SCI-JM. (2023); 30(4):381--389
Chicago/Turabian Style
Jamal, S., Champala, R.. "On the elliptical solutions of models connected to the short pulse equation." Journal of Mathematics and Computer Science, 30, no. 4 (2023): 381--389
Keywords
- Lie symmetries
- elastic beam equations
- sine-Gordon
MSC
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