Abstract
Soliton Equations as Dynamical Systems on Infinite Dimensional Grassmann Manifold The totality of the solutions of the Kadomtsev– Petviashvili equation as well as of its multicomponent generalization forms an infinite dimensional Grassmann manifold. In this picture, the time evolution of a solution is interpreted as the dynamical motion of a point on this manifold. A generic solution corresponds to a generic point whose orbit (in the infinitely many time variables) is dense in the manifold, whereas degenerate solutions corresponding to points bound on those closed submanifolds that are stable under the time evolution describe the solutions to various specialized equations, such as KdV, Boussinesq, nonlinear Schrödinger, and sine-Gordon.
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