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Wave propagation of nonlinear modes and formation of bubble in a two-component helicoidal lattice

  • Nonlinear Dynamics
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Abstract

Through the multiple scale expansion, we show that the dynamics of modulated waves in a two-component helicoidal one-dimensional model is governed by the nonlinear Schrödinger (NLS) equation. We study the occurrence of patterns formation in such a system. The impact of the helicoidal coupling is also studied which reveals that high values of the helicoidal coupling constant contribute to regulate information and charge transport throughout the two-chain model. This is made possible due to the superposition of optical and acoustic modes. In addition, the model is used to investigate internal dynamics of DNA. It is shown that the opening of the double helix of the DNA itself is controlled by the resonance mode, where the unzipping of the double helix has been illustrated by numerical simulations. Furthermore, the shape of the eyelike shape previously observed in experiments of thermal denaturation of DNA is numerically obtained.

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References

  • J.C. Luke, Proc. R. Soc. London. Ser. A 292, 403 (1966)

    Google Scholar 

  • G. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974)

  • M.H. Hays, C.D. Levermore, P.D. Miller, Physica D 79, 1 (1994); M.H. Hays, C.D. Levermore, P.D. Miller, Physica D 85, 304E (1995); C.D. Levermore, J.G. Liu, Physica D 99, 191 (1997)

  • Y.S. Kivshar, S. Flach, Chaos 13, 586 (2003); S. Aubry, Physica D 103, 201 (1997); A.J. Sievers, J.B. Page, in Dynamical Properties of Solids. VII Phonon Physics The Cutting Edge, edited by G.K. Horton, A.A. Maradudin (Elsevier, Amsterdam, 1995)

  • E. Fermi, J. Pasta, S. Ulam, Los Alamos Science Laboratory Report No LA-1940 (1955) (unpublished), reprinted in Collected papers of E. Fermi, edited by E. Sergre (University of Chicago Press, Chicago, 1965)

  • K. Forinash, T. Creteny, M. Peyrard, Phys. Rev. E 55, 4740 (1997)

    Google Scholar 

  • M. Peyrard, A.R. Bishop, Phys. Rev. Lett. 62, 2755 (1989)

    Google Scholar 

  • S. Zdravković, M. Satarić, Phys. Scr. 64, 612 (2001); S. Zdravković, M. Satarić, J.A. Tuszyńki, J. Comput. Theor. Nanosci. 1, 171 (2004)

  • T. Dauxois, Phys. Lett. A 159, 390 (1991)

    Google Scholar 

  • M. Peyrard, private communication; G. Gaeta, Phys. Lett. A 172, 365 (1993); G. Gaeta, Phys. Lett. A 179, 167 (1993)

  • M. Peyrard, Nonlinearity 17, R1 (2004)

  • T. Dauxois, M. Peyrard, Phys. Rev. E 47, 684 (1993)

    Google Scholar 

  • W. Saenger, Principle of Nucleic Acid Structure (Springer-Verlag, Berlin, 1984)

  • S. Zdravković, M. Satarić, Europhys. Lett. 80, 38003 (2007); S. Zdravković, M. Satarić, Europhys. Lett. 78, 38004 (2007)

  • S. Cocco, M. Monasson, J.F. Marko, Phys. Rev. E 66, 051914 (2002)

    Google Scholar 

  • T. Dauxois, M. Peyrard, C.R. Willis, Physica D 57, 267 (1992)

    Google Scholar 

  • T. Dauxois, M. Peyrard, A.R. Bishop, Phys. Rev. E. 47, R44 (1993)

  • R.M. Haas, Phys. Rev. D 57, 7422 (1998)

    Google Scholar 

  • M. Gleiser, R.M. Haas, Phys. Rev. D 54, 1626 (1996)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, University of Yaounde I, Laboratory of Mechanics, P.O. Box 812, Yaounde, Cameroon

    C. B. Tabi & A. Mohamadou

  2. Department of Physics, Faculty of Science, University of Douala, Condensed Matter Laboratory, P.O. Box 24157, Douala, Cameroon

    A. Mohamadou & T. C. Kofané

  3. The Abdus Salam, International Center For Theoretical Physics, P.O. Box 586, Strada Costiera, 11, 34014, Trieste, Italy

    A. Mohamadou & T. C. Kofané

Authors
  1. C. B. Tabi
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  2. A. Mohamadou
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  3. T. C. Kofané
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Correspondence to A. Mohamadou.

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Tabi, C., Mohamadou, A. & Kofané, T. Wave propagation of nonlinear modes and formation of bubble in a two-component helicoidal lattice. Eur. Phys. J. D 50, 307–316 (2008). https://doi.org/10.1140/epjd/e2008-00237-5

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  • DOI: https://doi.org/10.1140/epjd/e2008-00237-5

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