The propagation of pulses in ideal nonlinear optical fibers without loss is governed by the nonlinear Schrrdinger equation (NLS). When considering realistic fibers one must examine perturbed NLS equations, with the particular perturbation depending on the physical situation that is being modeled. A common example is the complex Ginzburg-Landau equation (CGL), which is a dissipative perturbation...

We describe the spectrum of the k-form Laplacian on conformally cusp Riemannian manifolds. The essential spectrum is shown to vanish precisely when the k and k − 1 de Rham cohomology groups of the boundary vanish. We give Weyl-type asymptotics for the eigenvalue-counting function in the purely discrete case. In the other case we analyze the essential spectrum via positive commutator methods. We...