Generalized dispersion Kerr solitons

We report a continuum of pulse-like 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 new analytic solutions for positive quadratic dispersion and negative quartic dispersion, investigate the soliton dynamics, and assess the implications of these solutions for use in soliton lasers.