Abstract
The derivative nonlinear Schrodinger (DNLS) equation is a nonlinear dispersive model that appears in the description of wave propagation in a plasma. The existence of a Lagrangian and the invariant variational principle for two coupled equations are given. The two coupled equations is describing the nonlinear evolution of the Alfv,n wave with magnetosonic waves at much larger scale. A type of the coupled DNLS equations is studied by means of symbolic computation, which can describe the wave propagation in birefringent optical fibers. The functional integral corresponding to those equations is derived. We investigate the approximation solutions of the DNLS equation by choice of a trial function in the region of the rectangular box in two cases. By using this trial functions, the functional integral and the Lagrangian of the system without loss are found. The general case for the two-box potential can be obtained on the basis of a different ansatz, where we approximate the Jost function by series in the tanh function method instead of the piece-wise linear function.