Homoclinic solutions in mechanical systems with small dissipation. Application to DNA dynamics |
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Authors: | B Kazmierczak T Lipniacki |
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Institution: | Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska St. 21, 00-049 Warsaw, Poland. bkazmier@ippt.gov.pl |
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Abstract: | This paper analyzes the problem of persistence of homoclinic solutions to perturbed systems of second order ODE's. These
systems arise from PDE's, when considering solutions in the form of travelling waves. It is shown that homoclinic solutions
persist in the presence of dissipation. Dissipation can be balanced by nonautonomous terms of compact support, which are controlled
by a single parameter. This result is applied to prove the existence of torsional pulse-like travelling waves propagating
along a nonelastic DNA molecule. In this case the energy is added to system by advancing the RNA polymerase.
Received: 17 August 2000 / Revised version: 26 October 2001 / Published online: 14 March 2002 |
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