Interaction of two-dimensional Gaussian pulses in the media with cubic nonlinearity and negative dispersion

Interaction of two Gaussian pulses propagating in the media with cubic nonlinearity and negative group velocity dispersion is investigated in the case of one transverse dimension and one longitudinal dimension for the propagation axis. Variational approach (the so-called average Lagrangian method) is applied to the set of two coupled nonlinear Schrodinger equations with the ansatz in the form of two Gaussian pulses with the same center. It is shown that initial pulses collapse at the same point when propagating in the oscillation regime and at different points when propagating in the monotonous one. It is confirmed numerically that all the results are preserved when the group velocity coefficients are essentially different