Numerical resolution of some nonlinear Schrodinger-like equations in plasmas

Schrodinger-like equations play an essential role in the modeling of plasma s created by laser beams, and taking into account of relativistic terms yie lds anew kind of nonlinearity in them, as compared to the classical case. A numerical scheme involving a new handling of absorbing conditions suitable for Schrodinger-like equations is given, and several general models are st udied: the classical cubic case linked to the Kerr effect for an anharmonic plasma, where numerical experiments prove the efficiency of our code appli ed to the computation of solitons and explosive solutions. Furthermore, new kinds of explosive solutions are computed, and we numerically show the ess ential role of the ground state to get approximations of the cubic explosiv e solution by global ones. A multiphotonic ionization model is also studied including higher-order terms in the nonlinearity. In this case, we obtain stable structures physically explained by competing saturation processes. T hese structures have been experimentally detected. Finally, a relativistic model involving the Lorentz kinematic factor in the evolution equations is investigated numerically; filamentary structures are found in agreement wit h predicted relativistic phenomena. (C) 1999 John Wiley & Sons, Inc.