Generalized dispersion Kerr solitons

We report a continuum of pulselike soliton solutions to the generalized nonlinear Schrodinger equation with both quadratic and quartic dispersion and a Kerr nonlinearity. We show that the well-known nonlinear Schrodinger solitons, which occur in the presence of only negative (anomalous) quadratic dispersion, and pure-quartic solitons, which occur in the presence of only negative quartic dispersion, are members of a large superfamily, encompassing both. The members of this family, none of which are unstable, have exponentially decaying tails, which can exhibit oscillations. We find analytic solutions for positive quadratic dispersion and negative quartic dispersion and investigate the soliton dynamics. We also find evidence that a combination of the quadratic and quartic dispersion, rather than exclusively quadratic or quartic dispersion, is likely to improve the performance of soliton lasers.