Abstract:
The problem of a classification of integrable evolution equations on the\break N-dimensional sphere is considered. We modify the main notions of the symmetry approach such as the formal symmetry and the canonical series of conserved densities to the case of such equations. Using these theoretical results, we solve several special classification problems. The main result is a complete classification of integrable isotropic evolution equations of third order on the sphere. An important class of anisotropic equations is also considered.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 16 July 2001 / Accepted: 25 March 2002 Published online: 14 November 2002
Rights and permissions
About this article
Cite this article
Meshkov, A., Sokolov, V. Integrable Evolution Equations on the N-Dimensional Sphere. Commun. Math. Phys. 232, 1–18 (2002). https://doi.org/10.1007/s00220-002-0737-9
Issue Date:
DOI: https://doi.org/10.1007/s00220-002-0737-9