A Periodic Solution of the Newell-Whitehead-Segel (NWS) Wave ‎Equation via Fractional Calculus

Document Type : Research Paper


Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt


The Newell-Whitehead-Segel (NWS) equation is one of the most significant amplitude equations with a wider practical applications in engineering and applied physics. It describes several line patterns; for instance, see lines from seashells and ripples in the sand. In addition, it has several applications in mathematical, chemical, and mechanical physics, as well as bio-engineering and fluid mechanics. Therefore, the current research is concerned with obtaining an approximate periodic solution of a nonlinear dynamical NWS wave model at three different powers. The fractional calculus via the Riemann-Liouville is adopted to calculate an analytical periodic approximate solution. The analysis aims to transform the original partial differential equation into a nonlinear damping Duffing oscillator. Then, the latter equation has been solved by utilizing a modified Homotopy perturbation method (HPM). The obtained results revealed that the present technique is a powerful, promising, and effective one to analyze a class of damping nonlinear equations that appears in physical and engineering situations.


Main Subjects

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