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