Fred Cooper (Los Alamos National Laboratory; SFI External Professor)
Abstract. Solitary waves occur in many nonlinear dynamical systems when there is a balance between dispersive forces and attractive forces. When these dynamical systems allow a Lagrangian or Hamiltonian formulation, then (time dependent) variational methods can be used to simplify our understanding of the general features of these waves and their stability properties without resorting to solving the underlying partial differential equations. We give examples from the Nonlinear Schrodinger equation, Generalized K-dV equations (compactors), Camassa- Holm Water-wave equation (peaked solitons) as well as the Nonlinear Dirac equation. We show how to determine the gross features of the solitary wave- such as the connection between the Height, width, Mass , energy and velocity as well as the stability properties of the solitary waves using both time-independent and time dependent variational methods.