Non-linear partial differential equations via vector fields on homogeneous Banach manifolds

✍ Scribed by Hongyou Wu

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 747 KB
• Volume: 10
• Category: Article
• ISSN: 0232-704X
• DOI: 10.1007/bf00130917

✦ Synopsis

The vector field formulation of and the Sato-Segal-Wilson approach to soliton equations are related to each other in this paper. From Banach Lie groups associated with the MKdV hierarchy of differential equations, we derive homogeneous Banach manifolds of solutions on which these equations are realized by vector fields. In the same way, we obtain homogeneous Banach manifolds of solutions to the sine-Gordon equation. The scattering and inverse scattering maps in this set-up are also discussed.