Solitary waves from optics to water waves

Optical fiber communications involves quite naturally the study of nonlinear waves. Asymptotic analysis leads to “classical”, and “dispersion managed” -nonlocal nonlinear Schrodinger equations which contain solitary waves as special solutions. A numerical method is introduced to find these and other solitary waves in optics. In water waves the classical equations are reformulated as integral equations on a fixed domain. Integral (conservation) relations are obtained. Asymptotic reductions of this system yields the Boussinesq/KdV, Benney-Luke/Kadomtsev-Petviashvili and nonlinear Schr"odinger equations. The above numerical method is extended to find two dimensional lumps with sufficient surface tension.