Applications of the series expansion unknown functions method in nonlinear dynamics of microtubules

TL;DR

This paper applies the series expansion unknown functions method to solve nonlinear differential equations in microtubule dynamics, comparing it with existing methods to identify its generality and effectiveness.

Contribution

It introduces the SEUFM as a new approach for solving nonlinear equations in microtubule models and compares its solutions with traditional methods.

Findings

SEUFM provides a more general solution framework.

Solutions are expressed as series expansions with unknown functions.

Comparison shows SEUFM's potential advantages over THFM and SEM.

Abstract

Microtubules (MTs) are the most important part of cytoskeleton. In this paper we deal with two basic nonlinear differential equations coming from the two known models describing nonlinear dynamics of MTs. These equations are solved using the series expansion unknown functions method (SEUFM). Trying to recognize the most general mathematical procedure for solving these equations the solutions are compared with those obtained earlier using the tangent hyperbolic function method (THFM) and the simplest equation method (SEM). In all these three approaches we express the solutions of these equations as series expansions. In the cases of THFM and SEM the functions existing in the series are known while SEUFM assumes unknown functions.