Conservation of the Cylindrical and Elliptic Cylindrical K-P Equations

Authors

Joseph Boon Zik Hong, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81300 Skudai, Johor, MalaysiaFollow
K. Fakhar, Mathematics Department, University of British Columbia, Vancouver, CanadaFollow
S. Ahmad, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81300 Skudai, Johor, MalaysiaFollow
A. H. Kara, School of Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa\\ Dept of Maths and Stats, King Fahd University of Petroleum and Minerals, Dhahran, Saudi ArabiaFollow

Author Country (or Countries)

Saudi Arabia

Abstract

We study the invariance properties and exact solutions of the Kadomtsev-Petviashvili equation and construct its conservation laws and that of its transformed elliptic and elliptic-cylindrical versions. Then, it is shown how the conservation laws and related quantities of the transformed versions may be attained by applying the transformation variables as opposed to independent calculations which are often cumbersome for high order partial differential equations of ‘many’ variables.

Recommended Citation

Boon Zik Hong, Joseph; Fakhar, K.; Ahmad, S.; and H. Kara, A. (2015) "Conservation of the Cylindrical and Elliptic Cylindrical K-P Equations," Applied Mathematics & Information Sciences: Vol. 09: Iss. 2, Article 11.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss2/11