Abstract:
A nonlinear wave is one of the basic objects of physics. They are inherent to plasma physics and
solid state physics, gravity and nuclear physics, field theory and optics, hydrodynamics and aerodynamics,
kinetics of chemical reactions and population dynamics. It is well known that the constuction of explicit
solutions for an integrable system plays a significant part in the definition and explanation of nonlinear
phenomena. In this article, we will focus on integrable nonlinear Schrodinger and Maxwell-Bloch equations
(NLS-MB) that represents the propagation of optical impulses in an inhomogeneous fibreglass with erbiumdoped losses or amplification due to an external potential. Lax representation of NLS-MB will be given.
Based on relevant Lax pair, Darboux transformation for NLS-MB will be obtained. Exact solutions will be
derived through the Darboux transformation. Graphs of the obtained solutions will be constructed. By using
our approach one can find also other differerent exact solutions of NLS-MB equations.
