Abstract
The enhanced modified simple equation method plays a vital role in finding an exact traveling wave solution of nonlinear evolution equations (NLEEs) in engineering and mathematical physics. In this article, we use the enhanced modified simple equation method to find the exact solutions of NLEEs via the Burger-Fisher equation and the modified Volterra equations and achieve exact solutions involving parameters. When the parameters receive special values, the solitary wave solutions are derived from the exact solutions. It is established that the enhanced modified simple equation method offers a further influential mathematical tool for constructing exact solutions of NLEEs in mathematical physics.
Highlights
It is well known that nonlinear phenomena occur in various areas of science and engineering, such as fluid mechanics, plasma, solid-state physics, biophysics, etc., and could be modeled by nonlinear evolution equations (NLEEs)
The issue is to look for exact solutions of NLEEs which can help understand that the internal mechanism of intricate physical phenomena plays a vital role
5 Conclusions In this letter, we considered the Burger-Fisher and the modified Volterra equations
Summary
It is well known that nonlinear phenomena occur in various areas of science and engineering, such as fluid mechanics, plasma, solid-state physics, biophysics, etc., and could be modeled by nonlinear evolution equations (NLEEs). Many powerful and efficient methods and techniques, such as Darboux transformations method [ ], Bäcklund transformation method [ ], Hirota’s bilinear method [ ], Painlevé expansions method [ ], symmetry method [ ], the tanh method [ ], the homogeneous balance method [ ], the Jacobi-elliptic function method [ ], the (G /G)-expansion method [ – ], F-expansion method [ ], the exp-expansion method [ , ], Exp-function method [ – ], the modified simple equation method [ – ], the generalized and improved (G /G)-expansion method [ ], and so on, were established to obtain exact traveling wave solutions of nonlinear physical phenomena. In Section , the enhanced modified simple equation method is discussed.
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