Abstract and Applied Analysis

Travelling Wave Solutions of Nonlinear Dynamical Equations in a Double-Chain Model of DNA

Zheng-yong Ouyang and Shan Zheng

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We consider the nonlinear dynamics in a double-chain model of DNA which consists of two long elastic homogeneous strands connected with each other by an elastic membrane. By using the method of dynamical systems, the bounded traveling wave solutions such as bell-shaped solitary waves and periodic waves for the coupled nonlinear dynamical equations of DNA model are obtained and simulated numerically. For the same wave speed, bell-shaped solitary waves of different heights are found to coexist.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 317543, 5 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425048256

Digital Object Identifier
doi:10.1155/2014/317543

Mathematical Reviews number (MathSciNet)
MR3193500

Zentralblatt MATH identifier
07022158

Citation

Ouyang, Zheng-yong; Zheng, Shan. Travelling Wave Solutions of Nonlinear Dynamical Equations in a Double-Chain Model of DNA. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 317543, 5 pages. doi:10.1155/2014/317543. https://projecteuclid.org/euclid.aaa/1425048256


Export citation

References

  • J. D. Watson and F. H. C. Crick, “Molecular structure of nucleic acids: a structure for deoxyribose nucleic acid,” Nature, vol. 171, no. 4356, pp. 737–738, 1953.
  • M. Peyrard, S. C. López, and G. James, “Modelling DNA at the mesoscale: a challenge for nonlinear science?” Nonlinearity, vol. 21, p. T91, 2008.
  • T. Lipniacki, “Chemically driven traveling waves in DNA,” Physical Review E, vol. 60, p. 7253, 1999.
  • S. Yomosa, “Solitary excitations in deoxyribonuclei acid (DNA) double helices,” Physical Review A, vol. 30, no. 1, pp. 474–480, 1984.
  • C. T. Zhang, “Soliton excitations in deoxyribonucleic acid (DNA) double helices,” Physical Review A, vol. 35, no. 2, pp. 886–891, 1987.
  • K. Forinash, “Nonlinear dynamics in a double-chain model of DNA,” Physical Review B, vol. 43, p. 10734, 1991.
  • L. V. Yakushevich, Nonlinear Physics of DNA, John Wiley & Sons, Berlin, Germany, 2004.
  • S. W. Englander, N. R. Kallenbanch, A. J. Heeger, J. A. Krumhansl, and S. Litwin, “Nature of the open state in long polynucleotide double helices: possibility of soliton excitations,” Proceedings of the National Academy of Sciences of the United States of America, vol. 77, pp. 7222–7226, 1980.
  • S. Yomosa, “Soliton excitations in deoxyribonucleic acid (DNA) double helices,” Physical Review A, vol. 27, no. 4, pp. 2120–2125, 1983.
  • S. Takeno and S. Homma, “A coupled base-rotator model for structure and dynamics of DNA–-local fluctuations in helical twist angles and topological solitons,” Progress of Theoretical Physics, vol. 72, no. 4, pp. 679–693, 1984.
  • M. Peyrard and A. R. Bishop, “Statistical mechanics of a nonlinear model for DNA denaturation,” Physical Review Letters, vol. 62, no. 23, pp. 2755–2758, 1989.
  • T. Dauxois, M. Peyrard, and A. R. Bishop, “Entropy-driven DNA denaturation,” Physical Review E, vol. 47, no. 1, pp. R44–R47, 1993.
  • V. Muto, P. S. Lomdahl, and P. L. Christiansen, “Two-dimensional discrete model for DNA dynamics: longitudinal wave propagation and denaturation,” Physical Review A, vol. 42, no. 12, pp. 7452–7458, 1990.
  • D. X. Kong, S. Y. Lou, and J. Zeng, “Nonlinear dynamics in a new double Chain-model of DNA,” Communications in Theoretical Physics, vol. 36, no. 6, pp. 737–742, 2001.
  • X.-M. Qian and S.-Y. Lou, “Exact solutions of nonlinear dynamics equation in a new double-chain model of DNA,” Communications in Theoretical Physics, vol. 39, no. 4, pp. 501–505, 2003.
  • W. Alka, A. Goyal, and C. Nagaraja Kumar, “Nonlinear dynamics of DNA–-riccati generalized solitary wave solutions,” Physics Letters A: General, Atomic and Solid State Physics, vol. 375, no. 3, pp. 480–483, 2011.
  • S. N. Chow and J. K. Hale, Methods of Bifurcation Theory, Springer, Berlin, Germany, 1981.
  • J. B. Li and Z. R. Liu, “Smooth and non-smooth traveling waves in a nonlinearly dispersive equation,” Applied Mathematical Modelling, vol. 25, pp. 41–56, 2000.
  • J. B. Li and Z. R. Liu, “Traveling wave solutions for a class of nonlinear dispersive equations,” Chinese Annals of Mathematics, vol. 23, p. 397, 2002.
  • Z. R. Liu and Z. Y. Ouyang, “A note on solitary waves for modified forms of Camassa-Holm and Degasperis-Procesi equations,” Physics Letters A, vol. 366, no. 4-5, pp. 377–381, 2007. \endinput