zbMATH — the first resource for mathematics

Banach manifolds of solutions to nonlinear partial differential equations, and relations with finite-dimensional manifolds. (English) Zbl 0798.58010
Greene, Robert (ed.) et al., Differential geometry. Part 1: Partial differential equations on manifolds. Proceedings of a summer research institute, held at the University of California, Los Angeles, CA, USA, July 8-28, 1990. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 54, Part 1, 121-139 (1993).
The author surveys some recent results interrelating classes of finite- dimensional manifolds, integrable systems, loop groups, and manifolds of solutions to certain nonlinear partial differential equations. These equations include the Korteweg-deVries equation (KdV), the modified Korteweg-deVries equation (MKdV), the nonlinear Schrödinger equation (NLS), and the sine-Gordon equation.
For the entire collection see [Zbl 0773.00022].

58D25 Equations in function spaces; evolution equations
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
58J99 Partial differential equations on manifolds; differential operators