Higher-dimensional spatiotemporal parametric solitons

Summary form only given.We consider solutions to the second-harmonic generation equations in twoand three-dimensional dispersive media, in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. We obtain the general solution in an approximate analytical form by means of a variational approach. Then, we directly simulate the two- and three-dimensional cases, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that stable spatiotemporal solitons indeed exist and are stable.