A variational approach to the nonlinear Schrodinger equation

A variational approach for finding approximate solutions of the NLS equation is presented. The approach is based on trial functions involving parameter functions which depend on the evolution coordinate. The parameter functions are determined using direct variational methods and Ritz optimization. Two illustrative examples are given. The first considers one-dimensional pulse propagation in dispersive and nonlinear optical fibres. The second concerns two-dimensional laser beam propagation in a medium with a refractive index radially inhomogeneous in the direction perpendicular to the direction of propagation. The usefulness and accuracy of the variational results are demonstrated by comparisons with numerical results and with result of the conventional paraxial ray approximation for nonlinear laser beam propagation.