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arXiv · 1807.01114

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

J. M. Conde·F. Güngör
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Abstract

The Lie algebra of the symmetry group of the $(n+1)$-dimensional ge\-ne\-ra\-li\-zation of the dispersionless Kadomtsev--Petviashvili (dKP) 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 $\Sl(2,\mathbb{R})$ 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.

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J. M. Conde, F. Güngör. 2018-11-03. Analysis of the symmetry group and exact solutions of the dispersionless KP equation in $n+1$ dimensions. https://doi.org/10.1063/1.5046929

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