The improved Riccati equation mapping method for constructing many families of exact solutions for a nonlinear partial differential equation of nanobiosciences

Abstract

In this paper we apply the improved Riccati equation mapping method to construct many families of general exact solutions of a nonlinear partial differential equation involving parameters of special significant for nanobiosciences and biophysics, namely, the equation of nano-ionic currents along microtublues. Comparison between our new results and the well-known results are given. The nonlinear equation elaborated here is quite original and proposed in the context of important nanosciences problems related with cell signaling. It could be even of basic importance for explanation of congnitive processes in neurons. We can successfully recover the previously known exact solutions that have been found by other methods. The proposed method in this article can be applied to many other nonlinear partial differential equations.   Key words: Improved Riccati equation mapping method, exact traveling wave solutions, nonlinear partial differential equation of nano-ionic currents along  microtublues.