Algebraic and geometric space-time analogies in nonlinear optical pulse propagation

We extend recently developed algebraic space-time analogies for the dispers ive and nonlinear propagation of optical breathers. Geometrical arguments c an explain the similarity of evolutionary behavior between spatial and temp oral phenomena even when strict algebraic translation of solutions may not be possible. This explanation offers a new set of tools for understanding a nd predicting the evolutionary structure of self-consistent Gaussian breath ers in nonlinear optical fibers. (C) 2001 Optical Society of America.