Numerical study of self-focusing solutions to the Schrödinger-Debye system (Q2709436)

The authors implement different numerical schemes to simulate the equations of Schrödinger-Debye in nonlinear optics. Their main interest is in finding numerical evidence of the existence of blow-up solutions, i.e. solutions that become infinite in finite time. The existence of such solutions is an open problem.NEWLINENEWLINENEWLINEThe two methods used are a relaxation scheme and a split-step method. Both are classical methods to deal with nonlinear Schrödinger equations but they are not of the same type. Both methods give analogous result that suggest that there are, indeed, blow-up solutions. This probably indicates that the two methods reflect the real behaviour of the continuous equations and not numerical artifacts.