Nonsymmetric moving breather collisions in the Peyrard-Bishop DNA model

Azucena Álvarez; Francisco R. Romero; José M. Romero; Juan F. R. Archilla

doi:10.3934/dcdss.2011.4.995

Article Contents

2011, Volume 4, Issue 5: 995-1006. Doi: 10.3934/dcdss.2011.4.995

This issue Previous Article Asymptotics for supersonic traveling waves in the Morse lattice Next Article Existence of solitary waves in nonlinear equations of Schrödinger type

Nonsymmetric moving breather collisions in the Peyrard-Bishop DNA model

1.
Grupo de Física No Lineal. Facultad de Física. Universidad de Sevilla, Avda. Reina Mercedes, s/n. 41012-Sevilla
2.
Grupo de Física No Lineal. ETSII. Universidad de Sevilla, Avda. Reina Mercedes, s/n. 41012-Sevilla

Received: September 30, 2009

Revised: January 31, 2010

Published: September 2011

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Abstract

We study nonsymmetric collisions of moving breathers (MBs) in the Peyrard-Bishop DNA model. In this paper we have considered the following types of nonsymmetric collisions: head-on collisions of two breathers traveling with different velocities; collisions of moving breathers with a stationary trapped breather; and collisions of moving breathers traveling with the same direction. The various main observed phenomena are: one moving breather gets trapped at the collision region, and the other one is reflected; breather fusion without trapping, with the appearance of a new moving breather; and breather generation without trapping, with the appearance of new moving breathers traveling either with the same or different directions. For comparison we have included some results of a previous paper concerning to symmetric collisions, where two identical moving breathers traveling with opposite velocities collide. For symmetric collisions, the main observed phenomena are: breather generation with trapping, with the appearance of two new moving breathers with opposite velocities and a stationary breather trapped at the collision region; and breather generation without trapping, with the appearance of new moving breathers with opposite velocities. A common feature for all types of collisions is that the collision outcome depends on the internal structure of the moving breathers and the exact number of pair-bases that initially separates the stationary breathers when they are perturbed. As some nonsymmetric collisions result in the generation of a new stationary trapped breather of larger energy, the trapping phenomenon could play an important part of the complex mechanisms involved in the initiation of the DNA transcription processes.

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Mathematics Subject Classification: Primary: 70Kxx, 82C22; Secondary: 92D20.

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