SIAM Journal on Applied Mathematics, Vol. 59, No. 6 (Aug. - Oct., 1999), pp. 2139-2161 (23 pages) Considered here is a model equation put forward by Benjamin that governs approximately the evolution ...

We construct explicit solutions of the inhomogeneous parabolic wave equation in a linear and quadratic approximation. As examples, oscillating laser beams in a 1D parabolic waveguide, spiral light ...