Abstract
This article presents a numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit h [rightward arrow] 0 of the nonlinear paraxial equation. In a general setting of both dimension and nonlinearity, the essential differences between the ââ"šÂ¬Ã…"defocusingââ"šÂ¬Ã‚ and ââ"šÂ¬Ã…"focusingââ"šÂ¬Ã‚ cases are observed. Numerical comparisons of the oscillations are made between the linear (ââ"šÂ¬Ã…"freeââ"šÂ¬Ã‚Â) 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 characterization of the weak limits of the oscillations in the defocusing case.
| Original language | English |
|---|---|
| Number of pages | 5 |
| Journal | Laser and Particle Beams |
| Publication status | Published - 2004 |
Keywords
- laser-plasma interactions
- nonlinear paraxial equation
- oscillations
- wave propagation