Focusing and defocusing of the nonlinear paraxial equation at laser-plasma interaction

This paper presents a numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit tau --> 0 of the nonlinear paraxial equation at laser-plasma interaction. In a general setting of both dimension and nonlinearity, the essential differences between the focusing and defocusing cases is identified due to the nonlinearity, and dispersion effects involved in the propagation of solitons at laser plasma interaction. A sequence of codes has been developed in mathematics to explore the focusing and defocusing of the soliton formation and propagation.