It is shown that the problem of dispersive self-modulation of waves including one transverse dimension and the three-dimensional self-focusing and self-defocusing theories has exact nontrivial analytic solutions. These are solutions compatible with cylindrical geometry and self-similar solutions that describe intermediate asymptotic, or long-time, behavior. These solutions are all obtained from symmetry considerations only.
© 1990 Optical Society of America
Original Manuscript: May 11, 1989
Manuscript Accepted: December 5, 1989
Published: June 1, 1990
L. Gagnon, "Exact solutions for optical wave propagation including transverse effects," J. Opt. Soc. Am. B 7, 1098-1102 (1990)