The generalized Davey-Stewartson equations, its Kac-Moody-Virasoro symmetry algebra and relation to Davey-Stewartson equations

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Gungor F., Aykanat O.

JOURNAL OF MATHEMATICAL PHYSICS, vol.47, no.1, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.1063/1.2162147
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Istanbul Technical University Affiliated: No


We compute the Lie symmetry algebra of the generalized Davey-Stewartson (GDS) equations and show that under certain conditions imposed on parameters in the system it is infinite-dimensional and isomorphic to that of the standard integrable Davey-Stewartson equations which is known to have a very specific Kac-Moody-Virasoro loop algebra structure. We discuss how the Virasoro part of this symmetry algebra can be used to construct new solutions, which are of vital importance in demonstrating existence of blow-up profiles, from known ones using Lie subgroup of transformations generated by three-dimensional subalgebras, namely sl(2,R). We further discuss integrability aspects of GDS equations. (c) 2006 American Institute of Physics.