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Symbolic computation of some new nonlinear partial differential equations of nanobiosciences using modified extended tanh-function method. (English) Zbl 1238.92001
Summary: By means of computerized symbolic computations and a modified extended tanh-function method multiple travelling wave solutions of nonlinear partial differential equations are presented and implemented in a computer algebraic system. Applying this method, we consider some 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. They 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 can also be applied to other nonlinear equations in physics.
MSC:
92C05Biophysics
35Q92PDEs in connection with biology and other natural sciences
68W30Symbolic computation and algebraic computation
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References:
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