Analysis of the symmetry group and exact solutions of the dispersionless KP equation in n+1 dimensions


Conde J. M. , Gungor F.

JOURNAL OF MATHEMATICAL PHYSICS, vol.59, no.11, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 11
  • Publication Date: 2018
  • Doi Number: 10.1063/1.5046929
  • Title of Journal : JOURNAL OF MATHEMATICAL PHYSICS

Abstract

The Lie algebra of the symmetry group of the (n + 1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili equation is obtained and identified as a semi-direct sum of a finite dimensional simple Lie algebra and an infinite dimensional nilpotent subalgebra. Group transformation properties of solutions under the subalgebra sl(2, R) are presented. Known explicit analytic solutions in the literature are shown to be actually group-invariant solutions corresponding to certain specific infinitesimal generators of the symmetry group. Published by AIP Publishing.