  Darboux transformation is one of the methods used in solving nonlinear
evolution equation. Basically, the Darboux transformation is a linear algebra
formulation of the solutions of the Zakharov-Shabat system of equations
associated with the nonlinear evolution equation. In this work, the evolution
of monochromatic electromagnetic wave in a nonlinear-dispersive optical medium
is considered. Using the Darboux transformation, explicit multisoliton
solutions (one to three soliton solutions) are obtained from a trivial initial
solution.
