Abstract
There has been considerable interest in seeking exact solutions of non-linear evolution equations that describe important physical and biological processes. Nonetheless, it is a difficult undertaking to determine closed form solutions of mathematical models that describe natural phenomena. This is because of their high non-linearity and the huge number of parameters of which they consist. In this article we determine, using the hyperbolic tangent (tanh) method, travelling wave solutions to non-linear evolution models of interest in biology and physics. These solutions have recognizable properties expected of other solutions and thus can be used to deduce properties of the general solutions.
Highlights
The study of non-linear partial differential equations is an important area of research in applied mathematics, theoretical physics and engineering
A powerful and effective technique called the hyperbolic tangent method helps in finding exact solutions of non-linear differential equations which allows all solitary and shock wave solutions to be obtained [10]
The main advantage of this method is that it helps to find exact solutions of higher non-linear evolution equations which are of fundamental importance
Summary
The study of non-linear partial differential equations is an important area of research in applied mathematics, theoretical physics and engineering. A powerful and effective technique called the hyperbolic tangent (tanh) method helps in finding exact solutions of non-linear differential equations which allows all solitary and shock wave solutions to be obtained [10]. The main advantage of this method is that it helps to find exact solutions of higher non-linear evolution equations which are of fundamental importance. This technique is straightforward and only minimal algebra is required. The main idea of this method is to express the solution of the non-linear differential equation as a polynomial. It is based on the homogeneous balance principle [11]. The aim of this study, is to determine analytic solutions to some useful mathematical models in biosciences and physics using the tanh method and to demonstrate how powerful, yet easy, the method is
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