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

TL;DR

This paper explores how Jacobian elliptic functions can be applied to solve specific nonlinear differential equations in microtubule dynamics, identifying which functions are suitable and analyzing soliton solutions.

Contribution

It demonstrates the applicability of Jacobian elliptic functions to solve ODEs in microtubule nonlinear dynamics and clarifies which functions are appropriate for these solutions.

Findings

Only one Jacobian elliptic function effectively solves the key differential equation.

A kink-type soliton propagates along microtubules.

Certain Jacobian elliptic functions do not represent valid solutions.

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.