A Hamiltonian Approach to Wave Modulation

The following sections are included:

• Introduction

• Periodic Solutions

  • The Hamiltonian Restricted to Periodic Solutions

  • The Symplectic Structure Restricted to Periodic Solutions

  • The Action of Periodic Orbits

• Modulations

  • Stationary Phase Integrals

  • The Modulational Poisson Brackets

  • The Modulational Hamiltonian

• Global Symmetry Implies Local Conservation Law

• The Nonlinear Klein-Gordon Equation