Mel'nikov Analysis of a Hamiltonian Perturbation of the Nonlinear Schr Odinger Equation

Homoclinic varieties play a crucial role in the dynamics of perturbations of the focusing Nonlinear Schrr odinger equation (NLS). We undertake a Mel'nikov analysis to investigate the possibility of persistence of transversal homoclinic orbits for a conservative perturbation of the NLS.