Optical temporal solitons, arising from self-phase modulation and negative quadratic (${\beta }_2$) dispersion, are Galilean invariant, and therefore their properties do not depend on their group velocity. This is no longer true for pure-quartic soliton pulses arising from quartic (${\beta }_4$) dispersion, for which a change in group velocity necessarily leads to nonzero quadratic and cubic (${\beta }_3$) dispersion. Analyzing the generalized nonlinear Schrödinger equation for such dispersion relations analytically and numerically, we find that pure-quartic solitons are members of a larger family traveling at other speeds. These solitons, which appear to be stable, have a complex phase structure and have an asymmetric spectrum. Our results extend the understanding of solitons arising from high orders of dispersion.

• Received 7 August 2021
• Accepted 14 October 2021

DOI:https://doi.org/10.1103/PhysRevA.104.043526