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Schubart-like orbits in the Newtonian collinear four-body problem: A variational proof
Breather continuation from infinity in nonlinear oscillator chains
1. | Laboratoire Jean Kuntzmann, UMR CNRS 5224, BP 53, 38041 Grenoble Cedex 9, France |
2. | Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada |
References:
[1] |
J. F. R. Archilla, J. Cuevas, B. Sánchez-Rey and A. Alvarez, Demonstration of the stability or instability of multibreathers at low coupling, Physica D, 180 (2003), 235-255. |
[2] |
S. Aubry, Breathers in nonlinear lattices: Existence, linear stability and quantization, Lattice Dynamics (Paris, 1995), Physica D, 103 (1997), 201-250.
doi: 10.1016/S0167-2789(96)00261-8. |
[3] |
S. Aubry, G. Kopidakis and V. Kadelburg, Variational proof for hard discrete breathers in some classes of Hamiltonian dynamical systems, Discrete and Continuous Dynamical Systems B, 1 (2001), 271-298. |
[4] |
D. Bambusi, Exponential stability of breathers in Hamiltonian networks of weakly coupled oscillators, Nonlinearity, 9 (1996), 433-457.
doi: 10.1088/0951-7715/9/2/009. |
[5] |
J. Fura and S. Rybicki, Periodic solutions of second order Hamiltonian systems bifurcating from infinity, Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, 24 (2007), 471-490. |
[6] |
G. James, Centre manifold reduction for quasilinear discrete systems, J. Nonlinear Sci., 13 (2003), 27-63.
doi: 10.1007/s00332-002-0525-x. |
[7] |
G. James, A. Levitt and C. Ferreira, Continuation of discrete breathers from infinity in a nonlinear model for DNA breathing, Applicable Analysis, 89 (2010), 1447-1465.
doi: 10.1080/00036810903437788. |
[8] |
G. James, B. Sánchez-Rey and J. Cuevas, Breathers in inhomogeneous nonlinear lattices: An analysis via center manifold reduction, Rev. Math. Phys., 21 (2009), 1-59.
doi: 10.1142/S0129055X09003578. |
[9] |
V. Koukouloyannis and P. Kevrekidis, On the stability of multibreathers in Klein-Gordon chains, Nonlinearity, 22 (2009), 2269-2285.
doi: 10.1088/0951-7715/22/9/011. |
[10] |
R. S. MacKay and S. Aubry, Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators, Nonlinearity, 7 (1994), 1623-1643.
doi: 10.1088/0951-7715/7/6/006. |
[11] |
R. S. MacKay and J.-A. Sepulchre, Stability of discrete breathers, Localization in Nonlinear Lattices (Dresden, 1997), Physica D, 119 (1998), 148-162.
doi: 10.1016/S0167-2789(98)00073-6. |
[12] |
J. L. Marín and S. Aubry, Finite size effects on instabilities of discrete breathers, Physica D, 119 (1998), 163-174. |
[13] |
A. Mielke and C. Patz, Dispersive stability of infinite-dimensional Hamiltonian systems on lattices, Applicable Analysis, 89 (2010), 1493-1512.
doi: 10.1080/00036810903517605. |
[14] |
A. Pankov, "Travelling Waves and Periodic Oscillations in Fermi-Pasta-Ulam Lattices," Imperial College Press, London, 2005.
doi: 10.1142/9781860947216. |
[15] |
M. Peyrard, S. Cuesta-López and G. James, Modelling DNA at the mesoscale: A challenge for nonlinear science?, Nonlinearity, 21 (2008), T91-T100.
doi: 10.1088/0951-7715/21/6/T02. |
[16] |
M. Peyrard, S. Cuesta-López and G. James, Nonlinear analysis of the dynamics of DNA breathing, J. Biol. Phys., 35 (2009), 73-89.
doi: 10.1007/s10867-009-9127-2. |
[17] |
M. Peyrard, Nonlinear dynamics and statistical physics of DNA, Nonlinearity, 17 (2004), R1-R40.
doi: 10.1088/0951-7715/17/2/R01. |
[18] |
J.-A. Sepulchre and R. S. MacKay, Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators, Nonlinearity, 10 (1997), 679-713.
doi: 10.1088/0951-7715/10/3/006. |
[19] |
D. Treschev, Travelling waves in FPU lattices, Discrete and Continuous Dynamical Systems A, 11 (2004), 867-880.
doi: 10.3934/dcds.2004.11.867. |
[20] |
G. Weber, Sharp DNA denaturation due to solvent interaction, Europhys. Lett., 73 (2006), 806.
doi: 10.1209/epl/i2005-10466-6. |
show all references
References:
[1] |
J. F. R. Archilla, J. Cuevas, B. Sánchez-Rey and A. Alvarez, Demonstration of the stability or instability of multibreathers at low coupling, Physica D, 180 (2003), 235-255. |
[2] |
S. Aubry, Breathers in nonlinear lattices: Existence, linear stability and quantization, Lattice Dynamics (Paris, 1995), Physica D, 103 (1997), 201-250.
doi: 10.1016/S0167-2789(96)00261-8. |
[3] |
S. Aubry, G. Kopidakis and V. Kadelburg, Variational proof for hard discrete breathers in some classes of Hamiltonian dynamical systems, Discrete and Continuous Dynamical Systems B, 1 (2001), 271-298. |
[4] |
D. Bambusi, Exponential stability of breathers in Hamiltonian networks of weakly coupled oscillators, Nonlinearity, 9 (1996), 433-457.
doi: 10.1088/0951-7715/9/2/009. |
[5] |
J. Fura and S. Rybicki, Periodic solutions of second order Hamiltonian systems bifurcating from infinity, Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, 24 (2007), 471-490. |
[6] |
G. James, Centre manifold reduction for quasilinear discrete systems, J. Nonlinear Sci., 13 (2003), 27-63.
doi: 10.1007/s00332-002-0525-x. |
[7] |
G. James, A. Levitt and C. Ferreira, Continuation of discrete breathers from infinity in a nonlinear model for DNA breathing, Applicable Analysis, 89 (2010), 1447-1465.
doi: 10.1080/00036810903437788. |
[8] |
G. James, B. Sánchez-Rey and J. Cuevas, Breathers in inhomogeneous nonlinear lattices: An analysis via center manifold reduction, Rev. Math. Phys., 21 (2009), 1-59.
doi: 10.1142/S0129055X09003578. |
[9] |
V. Koukouloyannis and P. Kevrekidis, On the stability of multibreathers in Klein-Gordon chains, Nonlinearity, 22 (2009), 2269-2285.
doi: 10.1088/0951-7715/22/9/011. |
[10] |
R. S. MacKay and S. Aubry, Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators, Nonlinearity, 7 (1994), 1623-1643.
doi: 10.1088/0951-7715/7/6/006. |
[11] |
R. S. MacKay and J.-A. Sepulchre, Stability of discrete breathers, Localization in Nonlinear Lattices (Dresden, 1997), Physica D, 119 (1998), 148-162.
doi: 10.1016/S0167-2789(98)00073-6. |
[12] |
J. L. Marín and S. Aubry, Finite size effects on instabilities of discrete breathers, Physica D, 119 (1998), 163-174. |
[13] |
A. Mielke and C. Patz, Dispersive stability of infinite-dimensional Hamiltonian systems on lattices, Applicable Analysis, 89 (2010), 1493-1512.
doi: 10.1080/00036810903517605. |
[14] |
A. Pankov, "Travelling Waves and Periodic Oscillations in Fermi-Pasta-Ulam Lattices," Imperial College Press, London, 2005.
doi: 10.1142/9781860947216. |
[15] |
M. Peyrard, S. Cuesta-López and G. James, Modelling DNA at the mesoscale: A challenge for nonlinear science?, Nonlinearity, 21 (2008), T91-T100.
doi: 10.1088/0951-7715/21/6/T02. |
[16] |
M. Peyrard, S. Cuesta-López and G. James, Nonlinear analysis of the dynamics of DNA breathing, J. Biol. Phys., 35 (2009), 73-89.
doi: 10.1007/s10867-009-9127-2. |
[17] |
M. Peyrard, Nonlinear dynamics and statistical physics of DNA, Nonlinearity, 17 (2004), R1-R40.
doi: 10.1088/0951-7715/17/2/R01. |
[18] |
J.-A. Sepulchre and R. S. MacKay, Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators, Nonlinearity, 10 (1997), 679-713.
doi: 10.1088/0951-7715/10/3/006. |
[19] |
D. Treschev, Travelling waves in FPU lattices, Discrete and Continuous Dynamical Systems A, 11 (2004), 867-880.
doi: 10.3934/dcds.2004.11.867. |
[20] |
G. Weber, Sharp DNA denaturation due to solvent interaction, Europhys. Lett., 73 (2006), 806.
doi: 10.1209/epl/i2005-10466-6. |
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