International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 210304, 16 pages
doi:10.1155/2009/210304

Integrable equations and their evolutions based on intrinsic geometry of Riemann spaces

Abstract

The intrinsic geometry of surfaces and Riemannian spaces will be investigated. It is shown that many nonlinear partial differential equations with physical applications and soliton solutions can be determined from the components of the relevant metric for the space. The manifolds of interest are surfaces and higher-dimensional Riemannian spaces. Methods for specifying integrable evolutions of surfaces by means of these equations will also be presented.