Session 7E - Space and Basic.
ORAL session, Thursday morning, November 14
Majestic Ballroom, Adam's Mark
The nonlinear dispersion relation between the group velocity and laser amplitude of a class of one-dimensional isolated envelope solitons for modulated light pulse coupled to electron plasma waves has been found analytically for \epsilon^2=ømega_p^2/ømega^2 \ll 1, where ømega_p is the plasma frequency and ømega is the laser frequency. The solitons are classified by the integer N which is the number of nodes of the laser vector potential envelope. The shift in the nonlinear group velocity from the linear group velocity is given by \Delta/2, where the eigenvalue \Delta<1. The conventional N=0 soliton is the continuum limit \Delta \ll \epsilon^2, \Delta \propto \phi_0\propto A_0^2, where \phi_0 and A_0 are the maximum electrostatic and vector potential respectively. As the laser vector potential amplitude is increased, the continuum of eigenvalues \Delta ceases to exist and the first discrete axisymmetric soliton with N = 1 occurs at \Delta\simeq 0.5\,\epsilon^2. In the large N limit, \Delta \sim \epsilon^8/5 N^4/5 and \phi_0 \sim \epsilon^2 N^2. Unlike the case of N=0, the width w of the large N soliton increases with amplitude, w\propto\sqrt\phi_0. The amplitude and group velocity of the solitons with N \geq 1 are quantised. This agrees with the numerical results [1,2]. [1]. V. A. Kozlov et al., Sov. Phis. JETP 49, 75 (1979). [2]. P. K. Kaw, Phys. Rev. Lett. 68, 3172 (1992).