| 講演要旨： |
It is commonly known that the majority of nonlinear wave equations, either the continuous models or the discrete ones, is nonintegrable in the sense that no general exact solutions are available. The variational approximation provides us with a tool for the study of the pulse solutions and their dynamical properties, such as the
stability and the pulse-pulse interactions. Starting with an ansatz, or, the trial function with free parameters, we can analytically average the Lagrangian, further, obtain the evolution equations for these free parameters. We will illustrate this method with specific examples, such as, the φ4 equation, a regularized equation for the Fermi-Pasta-Ulam β chain, the nonlinear Schrödinger equation (NLS), the coupled nonlinear Schrödinger equation (CNLS) and the discrete nonlinear Schrödinger (DNLS) equation. |
