A precise form of the quantum-mechanical time-energy uncertainty relation is derived. For
any given initial state (density operator), time-dependent Hamiltonian, and subspace of …

One-dimensional chains are used as a fundamental model of condensed matter, and have
constituted the starting point for key developments in nonlinear physics and complex …

This volume presents recent progress in the theory of nonlinear dispersive equations,
primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing …

Existence of'breathers', that is, time-periodic, spatially localized solutions, is proved for a
broad range of time-reversible or Hamiltonian networks of weakly coupled oscillators. Some …

The book is devoted to partial differential equations of Hamiltonian form, close to integrable
equations. For such equations a KAM-like theorem is proved, stating that solutions of the …

The total number of such permutations is equal to (n—1)(«—2)/2. Some of them are rotations
(isomorphic to the addition of a constant to the residues modn). But it is not clear what …

We consider the problem of extending to PDEs Birkhoff normal form theorem on Hamiltonian
systems close to nonresonant elliptic equilibria. As a model problem we take the nonlinear …

Consider 1 D nonlinear Schrödinger equation (0.1) iu_t-u_ xx+ V (x) u+ ε ∂\rm H ∂ ̄ u= 0
and nonlinear wave equation (0.2) y_ tt-y_ xx+ ρ y+ ε F'(y)= 0 under Dirichlet boundary …

We study stability times for a family of parameter dependent nonlinear Schrödinger
equations on the circle, close to the origin. Imposing a suitable Diophantine condition (first …

has been in the of a Symmetry major ingredient development quantum perturba tion and it is
a basic of the of theory, ingredient theory integrable (Hamiltonian and of the the use in …