SYMMETRY CLASSES OF VARIABLE-COEFFICIENT NONLINEAR SCHRODINGER-EQUATIONS

A variable-coefficient nonlinear Schrodinger (VCNLS) equation, involvi ng three arbitrary complex functions of space-time (in 1 + 1 dimension s) is analysed from the point of view of its symmetries. All equations of the type studied having non-trivial Lie point symmetry groups G ar e identified. The symmetry group is shown to be at most five-dimension al and only when the equation is equivalent to the NLS equation itself or to a rather special complex Ginzburg-Landau equation. Lie point tr ansformations are used to obtain solutions of specific VCNLs equations that should be of interest in nonlinear optics or other branches of p hysics.