Symbolic computation of some new nonlinear partial differential equations of nanobiosciences using modified extended tanh-function method

Abstract

By means of computerized symbolic computation and a modified extended tanh-function method the multiple travelling wave solutions of nonlinear partial differential equations is presented and implemented in a computer algebraic system. Applying this method, we consider some of nonlinear partial differential equations of special interest in nanobiosciences and biophysics namely, the transmission line models of microtubules for nano-ionic currents. The nonlinear equations elaborated here are quite original and first proposed in the context of important nanosciences problems related with cell signaling. It could be even of basic importance for explanation of cognitive processes in neurons. As results, we can successfully recover the previously known solitary wave solutions that had been found by other sophisticated methods. The method is straightforward and concise, and it can also be applied to other nonlinear equations in physics. © 2011 Elsevier Inc. All rights reserved.