New Treatment of wave solutions of the nonlinear Burgers equation

Document Type : Research and Reference

Authors

1 Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

2 Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Abstract

The nonlinear partial differential equations face many obstacles due to the nonlinear terms. The numerical and approximate solutions are only possible to be obtained. Most of the previous problems which were described by the nonlinear Navier-Stokes, Burgers equations were solved approximately for long wavelengths and low Reynolds number. In this paper, the unsteady nonlinear Burgers equation is converted to the linear diffusion equation based on the concept of linear velocity operator for the first time. The obstacle in the nonlinear term is solved in the nonlinear Burgers equation on the basis of Mohammadein concept. The Burgers equation is studied in one dimension. The simplest analytical solution of linear Burgers equation is obtained by Picard method. The analytical and simplest solution is obtained in terms of fluid velocity. It is studied in normal scale. The fluid velocity is affected by fluid viscosity, time and wavelengths. The calculated results introduced the validity of the present model.

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