Quasiclassical localization of wave packets in nonlinear Schrödinger systems

We consider the nonlinear Schrödinger equation with several kinds of potentials. For studying the existence and stability of the wave packets that could support these systems, a certain functional is constructed, which in some manner possesses the properties of the Lyapunov functional for analyzing the existence and stability of solutions. The general case of potential is considered and the appearance of pulsons is shown. Then we propose three examples of nonlinear classical field theories with potentials that exhibit quartic, sextic and saturable nonlinearities. This method exhibits a criteria for determining quasiclassically the self-localization of wave packets in nonintegrable systems.