Weakly nonlinear wave packets and the nonlinear Schrodinger equation

This chapter describes weakly nonlinear wave packets. The primary model equation is the nonlinear Schrodinger (NLS) equation. Its derivation is presented for two systems : the Korteweg-de Vries equation and the water-wave problem. Analytical as well as numerical results on the NLS equation are reviewed. Several applications are considered, including the study of wave stability. The bifurcation of waves when the phase and the group velocities are nearly equal as well as the effects of forcing on the NLS equation are discussed. Finally, recent results on the effects of dissipation on the NLS equation are also given.