Abstract
We consider collisions of moving breathers (MBs) in the Peyrard-Bishop DNA model. Two identical stationary breathers, separated by a fixed number of pair-bases, are perturbed and begin to move approaching to each other with the same module of velocity. The outcome is strongly dependent of both the velocity of the MBs and the number of pair-bases that initially separates the stationary breathers. Some collisions result in the generation of a new stationary trapped breather of larger energy. Other collisions result in the generation of two new MBs. In the DNA molecule, the trapping phenomenon could be part of the complex mechanisms involved in the initiation of the transcription processes.
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References
Peyrard, M., Bishop, A.R.: Statistical mechanics of a nonlinear model for DNA denaturation. Phys. Rev. Lett. 62, 2755–2758 (1989)
Dauxois, T., Mackay, R.S., Tsironis, G.P.: Nonlinear Physics: Condensed Matter, Dynamical Systems and Biophysics - A Special Issue dedicated to Serge Aubry. Physica D 216, 1–246 (2006)
Kivshar, Y.S., Flach, S.: Nonlinear localized modes: physics and applications. Chaos 13, 586–799 (2003)
Flach, S., Mackay, R.S.: Localization in nonlinear lattices. Physica D 119, 1–238 (1999)
Flach, S., Willis, C.R.: Discrete breathers. Phys. Rep. 295, 181–264 (1998)
Aubry, S., Cretegny, T.: Mobility and reactivity of discrete breathers. Physica D 119, 34–46 (1998)
Dauxois, T., Peyrard, M., Willis, C.R.: Localized breather-like solution in a discrete Klein-Gordon model and application to DNA. Physica D 57, 267–282 (1992)
Dauxois, T., Peyrard, M., Bishop, A.R.: Dynamics and thermodynamics of a nonlinear model for DNA denaturation. Phys. Rev. E 47, 684–695 (1993)
Cuevas, J., Archilla, J.F.R., Gaididei, Y.B., Romero, F.R.: Moving breathers in a DNA model with competing short- and long-range dispersive interactions. Physica D 163, 106–126 (2002)
Alvarez, A., Romero, F.R., Archilla, J.F.R., Cuevas, J., Larsen, P.V.: Breather trapping and breather transmission in a DNA model with an interface. Eur. Phys. J. B 51, 119–130 (2006)
Marín, J.L., Aubry, S.: Breathers in nonlinear lattices: Numerical calculation from the anticontinuous limit. Nonlinearity 9, 1501–1528 (1996)
Dmitriev, S.V., Kevrekidis, P.G., Malomed, B.A., Frantzeskakis, D.J.: Two-soliton collisions in a near-integrable lattice system. Phys. Rev. E 68, 056603, 1–7 (2003)
Sanz-Serna, J.M., Calvo, M.P.: Numerical Hamiltonian problems. Chapman and Hall, Boca Raton (1994)
Alvarez, A., Romero, F.R., Cuevas, J., Archilla, J.F.R.: Discrete moving breather collisions in a Klein-Gordon chain of oscillators. Phys. Lett. A 372, 1256–1264 (2008)
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© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
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Alvarez, A., Romero, F.R., Cuevas, J., Archilla, J.F.R. (2009). Moving Breather Collisions in the Peyrard-Bishop DNA Model. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_39
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DOI: https://doi.org/10.1007/978-3-642-02466-5_39
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