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Chin. Phys. B, 2014, Vol. 23(2): 020504    DOI: 10.1088/1674-1056/23/2/020504
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Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules

Slobodan Zekovića, Annamalai Muniyappanb, Slobodan Zdravkovića, Louis Kavithab c
a Institut za nuklearne nauke Vinča, Laboratorija za atomsku fiziku 040, Univerzitet u Beogradu, Poštanski fah 522, 11001 Beograd, Serbia;
b Department of Physics, Periyar University, Salem-636 011, Tamilnadu, India;
c Center for Nanoscience and Nanotechnology, Periyar University, Salem-636 011, Tamilnadu, India
Abstract  We show how Jacobian elliptic functions (JEFs) can be used to solve ordinary differential equations (ODEs) describing the nonlinear dynamics of microtubules (MTs). We demonstrate that only one of the 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 MTs. Besides this solution, we also discuss a few more solutions that may or may not have physical meanings. Finally, we show what kind of ODE can be solved by using JEFs.
Keywords:  Jacobian elliptic functions      ordinary differential equations      microtubules      kink soliton     
Received:  03 April 2013      Published:  12 December 2013
PACS:  05.45.Yv (Solitons)  
  87.10.Ed (Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models)  
  87.15.-v (Biomolecules: structure and physical properties)  
Fund: Project supported by Serbian Ministry of Education and Sciences (Grant No. Ⅲ45010), UGC, NBHM, India (major research projects), BRNS, India (Young Scientist Research Award), ICTP, Italy (Junior Associateship) and UGC (Rajiv Gandhi National Fellowship).
Corresponding Authors:  Slobodan Zdravković     E-mail:  szdjidji@vinca.rs
About author:  05.45.Yv; 87.10.Ed; 87.15.-v

Cite this article: 

Slobodan Zeković, Annamalai Muniyappan, Slobodan Zdravković, Louis Kavitha Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules 2014 Chin. Phys. B 23 020504

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