The stability of 1-D soliton in transverse direction

Abstract

The complete characterization of the exact 1-D solitary wave solutions (both stationary and propagating) for light plasma coupled system have been studied extensively in the parameter space of light frequency and the group speed [Poornakala et al., Phys. Plasmas 9(5), 1820 (2002)]. It has been shown in 1-D that solutions with single light wave peak and paired structures are stable and hence long lived. However, solutions having multiple peaks of light wave are unstable due to Raman scattering instability [Saxena et al., Phys. Plasmas 14, 072307 (2007)]. Here, we have shown with the help of 2-D fluid simulation that single peak and paired solutions too get destabilized by the transverse filamentation instability. The numerical growth rates obtained from simulations is seen to compare well with the analytical values. It is also shown that multiple peaks solitons first undergo the regular 1-D forward Raman scattering instability. Subsequently, they undergo a distinct second phase of destabilization through transverse filamentation instability. This is evident from the structure as well as the plot of the perturbed energy which shows a second phase of growth after saturating initially. The growth rate of the filamentation instability being comparatively slower than the forward Raman instability this phase comes quite late and is clearly distinguishable.