  By using Modified simple equation method, we study the Cahn Allen equation
which arises in many scientific applications such as mathematical biology,
quantum mechanics and plasma physics. As a result, the existence of solitary
wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions
interms of hyperbolic solutions of the associated Cahn Allen equation are
characterized with some free parameters. Finally, the variety of structure and
graphical representation make the dynamics of the equations visible and
provides the mathematical foundation in mathematical biology, quantum mechanics
and plasma physics.
