The behaviour of solutions of the nonlinear paraxial equation due to laser atom interactions

This paper presents a numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit of ћ→0 of the Nonlinear Paraxial Equation. In a general setting of both dimension and nonlinearity, the essential differences between the "defocusing" and " focusing" cases. Numerical comparisons of the oscillations are made between the linear ("free") and the cubic (defocusing and focusing) cases in one dimension. The integrability of the one-dimensional cubic Nonlinear Paraxial Equation is exploited to give a complete global characterisation of the weak limits of the oscillations in the defocusing case. These processes are important for the scheme of laser fusion based on the scheme of the "fast ignitor"