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Travelling wave solutions for time-delayed nonlinear evolution equations. (English) Zbl 1189.35281
Summary: Time-delayed nonlinear evolution equations have a wide range of applications in science and engineering. In this paper, the $\left(\frac{{G}^{\text{'}}}{G}\right)$-expansion method is implemented to establish travelling wave solutions for time-delayed Burgers and time-delayed Burgers-Fisher equations. The travelling wave solutions are expressed by hyperbolic functions and trigonometric functions. The results reveal that $\left(\frac{{G}^{\text{'}}}{G}\right)$-expansion method is very effective and a powerful tool for solving nonlinear time-delayed evolution equations arising in mathematical physics.
##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35C07 Traveling wave solutions of PDE 35C09 Trigonometric solutions of PDE 35A24 Methods of ordinary differential equations for PDE