The Nonlinear Schrödinger Equation

Abstract

The nonlinear Schrödinger equation is an example of a universal nonlinearmodel that describes many physical nonlinear systems. The equationcan be applied to hydrodynamics, nonlinear optics, nonlinear acoustics,quantum condensates, heat pulses in solids and various other nonlinearinstability phenomena. In this short review I will present a derivationof the nonlinear Schrödinger equation in the framework of the generalHamiltonian formalism for nonlinear waves and analyze some of itsremarkable features. The modulation instability of plane waves andthe appearance of solitary waves will be analyzed. In addition, conservationlaws will be discussed.