Symmetry classes of variable coefficient nonlinear Schrodinger equations

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