Focusing and defocusing of the nonlinear paraxial equation at laser-plasmainteraction

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