Dynamics of three-dimensional spatiotemporal solitons in multimode waveguides

In this work, we present a detailed study of the dynamics and stability of fundamental spatiotemporal solitons emerging in multimode waveguides with a parabolic transverse profile of the linear refractive index. Pulsed beam propagation in these structures can be described by using a Gross–Pitaevskii equation with a two-dimensional parabolic spatial potential. Our investigations compare variational approaches, based on the Ritz optimization method, with extensive numerical simulations. We found that, with a Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low pulse energies, where our analytical results find a perfect agreement with the numerical simulations. However, with progressively increasing energies, solitons eventually undergo wave collapse: this occurs below the theoretical limit, which is predicted within the variational approach. In a self-defocusing scenario, a similar trend is found, where the good agreement persists for low energies. For large soliton energies, however, complex spatiotemporal dynamics emerge.