Continuation of discrete breathers from infinity in a nonlinear model for DNA breathing

References

• Peyrard , M and Bishop , AR . 1989 . Statistical mechanics of a nonlinear model for DNA denaturation . Phys. Rev. Lett. , 62 : 2755
   PubMed Web of Science ®Google Scholar
• Peyrard , M . 2004 . Nonlinear dynamics and statistical physics of DNA . Nonlinearity , 17 : R1 – R40 .
   Web of Science ®Google Scholar
• Dauxois , T , Peyrard , M and Bishop , AR . 1993 . Entropy-driven DNA denaturation . Phys. Rev. E , 47 ( 1 ) : R44 – R47 .
   Google Scholar
• Flach , S and Gorbach , A . 2008 . Discrete Breathers: Advances in Theory and Applications . Phys. Rep. , 467 : 1 – 116 .
   Web of Science ®Google Scholar
• Daumont , I , Dauxois , T and Peyrard , M . 1997 . Modulational instability: First step towards energy localization in nonlinear lattices . Nonlinearity , 10 : 617 – 630 .
   Google Scholar
• Ivanchenko , MV , Kanakov , OI , Shalfeev , VD and Flach , S . 2004 . Discrete breathers in transient processes and thermal equilibrium . Phys. D , 198 : 120 – 135 .
   Google Scholar
• Arioli , G and Szulkin , A . 1998 . Periodic motions of an infinite lattice of particles: The strongly indefinite case . Ann. Sci. Math. Québec , 22 : 97 – 119 .
   Google Scholar
• Aubry , S . 1997 . Breathers in nonlinear lattices: Existence, linear stability and quantization . Phys. D , 103 : 201 – 250 .
   Web of Science ®Google Scholar
• Aubry , S , Kopidakis , G and Kadelburg , V . 2001 . Variational proof for hard discrete breathers in some classes of Hamiltonian dynamical systems . Discrete Contin. Dyn. Syst. B , 1 : 271 – 298 .
   Web of Science ®Google Scholar
• James , G . 2003 . Centre manifold reduction for quasilinear discrete systems . J. Nonlinear Sci. , 13 : 27 – 63 .
   Web of Science ®Google Scholar
• James , G , Sánchez-Rey , B and Cuevas , J . 2009 . Breathers in inhomogeneous lattices: An analysis via center manifold reduction . Rev. Math. Phys. , 21 : 1 – 59 .
   Google Scholar
• MacKay , RS and Aubry , S . 1994 . Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators . Nonlinearity , 7 : 1623 – 1643 .
   Web of Science ®Google Scholar
• Pankov , A . 2005 . Travelling waves and Periodic Oscillations in Fermi-Pasta-Ulam Lattices , London : Imperial College Press .
   Google Scholar
• Sepulchre , J-A and MacKay , RS . 1997 . Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators . Nonlinearity , 10 : 679 – 713 .
   Web of Science ®Google Scholar
• Zevin , A . 1996 . Localization of periodic oscillations in discrete non-linear systems . J. Sound Vibration , 193 : 847
   Google Scholar
• Peyrard , M , Cuesta-López , S and James , G . 2008 . Modelling DNA at the mesoscale: A challenge for nonlinear science? . Nonlinearity , 21 : T91 – T100 .
   Web of Science ®Google Scholar
• Peyrard , M , Cuesta-López , S and James , G . 2009 . Nonlinear analysis of the dynamics of DNA breathing . J. Biol. Phys. , 35 : 73 – 89 .
   Google Scholar
• Fura , J and Rybicki , S . 2007 . Periodic solutions of second order Hamiltonian systems bifurcating from infinity . Ann. Inst. Henri Poincaré (C) Anal. Non Linéaire , 24 ( 3 ) : 471 – 490 .
   Google Scholar
• Chen , D , Aubry , S and Tsironis , GP . 1996 . Breather Mobility in Discrete φ4 Nonlinear Lattices . Phys. Rev. Lett. , 77 : 4776 – 4779 .
   PubMedGoogle Scholar
• Cretegny , T and Aubry , S . 1997 . Spatially inhomogeneous time-periodic propagating waves in anharmonic systems . Phys. Rev. B , 55 : R11929 – R11932 .
   Google Scholar
• Morgante , AM , Johansson , M , Aubry , S and Kopidakis , G . 2002 . Breather-phonon resonances in finite-size lattices: ‘Phantom breathers’? . J. Phys. A: Math. Gen. , 35 : 1 – 23 .
   Google Scholar
• Aubry , S and Abramovici , G . 1990 . Chaotic trajectories in the standard map . The concept of anti-integrability, Phys. D , 43 : 199 – 219 .
   Google Scholar
• Aubry , S . 1995 . Anti-integrability in dynamical and variational problems . Physica D , 86 : 284 – 296 .
   Google Scholar
• Ciarlet , PG . 1970 . Discrete maximum principle for finite-difference operators . Aequationes Math. , 4 : 338 – 352 .
   Google Scholar
• Arnold , VI . 1992 . Ordinary Differential Equations , Berlin : Springer .
   Google Scholar
• Kato , T . 1980 . Perturbation Theory for Linear Operators , Berlin : Springer Verlag .
   Google Scholar
• Chicone , C . 1999 . “ Ordinary Differential Equations with Applications ” . In Texts in Applied Mathematics , Vol. 34 , New York : Springer .
   Google Scholar
• Marín , JL and Aubry , S . 1996 . Breathers in nonlinear lattices: Numerical calculation from the anticontinuous limit . Nonlinearity , 9 : 1501 – 1528 .
   Google Scholar
• Dennis , JE Jr and Schnabel , RB . 1996 . “ Numerical methods for unconstrained optimization and nonlinear equations ” . In Classics in Applied Mathematics , Vol. 16 , Philadelphia : SIAM .
   Google Scholar