2018/07/31 by J. M. Conde, Juan M. Conde, F. Güngör
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Generalization #Group (periodic table) #Group theory #Infinitesimal #Invariant (physics) #Lie algebra #Lie group #Mathematical analysis #Mathematical physics #Mathematics #Nilpotent #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Subalgebra #Symmetry (geometry) #Symmetry group #msc:35Q35 #msc:37K30 #msc:37K40 #nlin.SI
paper · pdf · doi:10.1063/1.5046929
published as J. Math. Phys. 59, 111501 (2018) · 13 pages
openalex created_date 2018/07/10 · openalex publication_date 2018/11/01 · arxiv created 2018/11/03 · arxiv updated 2018/11/06 · openalex updated_date 2026/08/05
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.