We report a continuum of pulse-like soliton solutions to the generalized nonlinear Schrödinger equation with both quadratic and quartic dispersion and a Kerr nonlinearity. We show that the well-known nonlinear Schrödinger 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 and investigate the soliton dynamics. We also find evidence that a combination of the quadratic and quartic dispersion, rather than exclusively quadratic dispersion, is likely to improve the performance of soliton lasers.
We numerically solve a generalized nonlinear Schrödinger equation and find a family of purequartic solitons, existing through a balance of positive Kerr nonlinearity and negative quartic dispersion. These solitons have oscillatory tails, which can be understood analytically from the properties of linear waves with quartic dispersion. By computing the linear eigenspectrum of the solitons, we show that they are stable, but that they possess a nontrivial internal mode close to the radiation continuum. We also demonstrate evolution into a pure-quartic soliton from Gaussian initial conditions. The energy-width scaling of pure-quartic solitons differs strongly from that for conventional solitons, opening possibilities for pure-quartic soliton lasers.
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