Abstract
In this paper we apply the improved Riccati equation mapping method to construct many families of exact solutions of a nonlinear partial differential equation involving parameters of a special interest in nanobiosciences and biophysics which describe a model of microtubules as nonlinear RLC transmission lines. As results, we can successfully recover the previously known results that have been found using other methods. This method is straightforward and concise, and it can be applied to other nonlinear PDEs in mathematical physics. Comparison between our new results and the well-known results are given. Some comments on the well-known results are also presented at the end of this article. Key words: Improved Riccati equation mapping method, exact traveling wave solutions, nonlinear partial differential equations (PDEs) of microtubules, Nonlinear RLC transmission lines. PACS: 02.30.Jr, 05.45.Yv, 02.30.Ik
Highlights
The exact traveling wave solutions for nonlinear partial differential equations (PDEs) has been investigated by many authors who are interested in non linear physical phenomena
We shall use the improved Riccati equation mapping method to find the exact solutions of a nonlinear PDE of nanobiosciences
Equation (2.1) using the improved Riccati equation mapping method (Zhu 2008; Zayed and Arnous, 2013; Zayed et al, 2013): Step 1: We look for its traveling wave solution in the form u ( x,t ) u ( ), kx t where k, are constants
Summary
The exact traveling wave solutions for nonlinear partial differential equations (PDEs) has been investigated by many authors who are interested in non linear physical phenomena. We shall use the improved Riccati equation mapping method to find the exact solutions of a nonlinear PDE of nanobiosciences. The main idea of this method is that the traveling wave solutions of nonlinear equations can be expressed by polynomials in Q , where. Riccati equation mapping method for finding many families of exact traveling wave solutions of the following nonlinear PDE of special interest in nanobiosciences, namely, the transmission line models for microtubules as nonlinear RLC transmission line (Sekulic et al, 2011a, Sataric et al, 2010):. Equation (1) has been discussed in (Sekulic et al 2011a) by using the modified extended tanh-function method, where its exact solutions have been found
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