Conservative perturbations of infinite-dimensional linear systems depending on a vector parameter
The starting point for this analysis is an infinite dimensional linear Hamiltonian system on some Hilbert space, which depends on n real parameters and whose almost periodic trajectories densely fill analytic invariant n-tori. The purpose is to state conditions under which these tori survive conservative perturbations for most parameter values. The formulation of the theorem in question is very technical, but it is essentially a generalization of a result proved in an earlier paper [\textit{S. B. Kuksin}, Funkts. Anal. Prilozh. 21, No.3, 22-37 (1987; Zbl 0631.34069)]. The present extension applies to such cases as the nonlinear Schrödinger equation and the KdV-equation.
infinite dimensional linear Hamiltonian system
scientific article; zbMATH DE number 4128126