By using Modified simple equation method, we study the Cahn Allen equationwhich arises in many scientific applications such as mathematical biology,quantum mechanics and plasma physics. As a result, the existence of solitarywave solutions of the Cahn Allen equation is obtained. Exact explicit solutionsinterms of hyperbolic solutions of the associated Cahn Allen equation arecharacterized with some free parameters. Finally, the variety of structure andgraphical representation make the dynamics of the equations visible andprovides the mathematical foundation in mathematical biology, quantum mechanicsand plasma physics.
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