Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules

Abstract

We show how Jacobian elliptic functions (JEF) can be used to solve ordinary differential equations (ODE) describing nonlinear dynamics of microtubules (MT). We demonstrate that only one of JEFs can be used while the remaining two do not represent the solutions of the crucial differential equation. We show that a kink-type soliton moves along MT. Beside this solution, we discuss a few more that may or may not have physical meaning. Finally, we show what kinds of ODE can be solved using JEFs.