On a new approach to the simulation of the nonlinear propagation of ultrashort laser pulses (Q1571165)

A new approach is suggested for the simulation of the interaction between femtosecond (ultrashort) light pulses and matter, which is based on the transformation of the initial generalized Schrödinger equation to a form convenient for constructing difference schemes based on the principle of conservativity. Construction of nonlinear difference schemes is demonstrated through an example of Kerr's nonlinearity. These schemes have known estimations for the rate of convergence of iterative processes and convergence of the difference solution to the analytical one.