In this work, we study the laser propagation in a thermonuclear
plasma corresponding to implosion of deuterium-tritium pellets
in inertial confinement fusion, by injecting energy provided
by high-power laser devices into a quiescent plasma and generating
solitons. Having in mind that the electric field inside of plasma
can be studied by means of a particular non-linear Schrödinger
equation, we solve this equation as an inverse problem, using
the Inverse Scattering Transform method, that is a 2 ×
2 eigenvalue problem, known as the AKNS scheme, developed by
Ablovitz, Kamp, Newell, and Shabat. We obtain the pseudopotentials
q and r if we suppose that the eigenvalue
is invariant in time, and is representative of a wave eigenvector,
obtaining a solution that has a structure of the soliton type.
In the process, one change of variable for space and another
for time are applied, and the relation between the pseudopotentials
is given by r = −q*. Discretization
of the non-linear Schrödinger equation, solved by inverse scattering
transform are given by Ablovitz et al. (1999). These solitons
are generated near the critical layer where w0
≅ wp, w0 being the
laser frequency and wp the plasma frequency,
exhibit a change in electronic density profile and are caused
by the ponderomotive force of laser radiation.