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Exp-function method for solving Huxley equation. (English) Zbl 1151.92007

Summary: The Huxley equation is a core mathematical framework for modern biophysically based neural modeling. It is often useful to obtain a generalized solitary solution for fully understanding its physical meanings. There are many methods to solve the equation, but each method can only lead to a special solution. This paper suggests a relatively new method, called the Exp-function method, for this purpose. The obtained result includes all solutions in the open literature as special cases, and the generalized solution with some free parameters might imply some fascinating meanings hidden in the Huxley equation.

MSC:

92C20 Neural biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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