We introduce an adaptive method for solving singular problems. In particular, the method can be applied to the simulations of nonlinear propagation of intense ultrafast laser pulses. This is a hard problem, because of the steep spatial gradients and the temporal shocks that form during the propagation. In this study we adapt the iterative grid distribution method [2] to solve the two-dimensional nonlinear Schrodinger equation with normal time dispersion, space-time focusing and self-steepening. Our simulations show that after the asymmetric temporal pulse splitting, the rear peak self-focuses faster than the front one. As a result, collapse of the rear peak is arrested before that of the front peak. Unlike what has been sometimes conjectured, however, collapse of the two peaks is not arrested through multiple splittings, but rather through temporal dispersion.
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