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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, Spain, Spain |
2. | Grupo de Física No Lineal. ETSII. Universidad de Sevilla, Avda. Reina Mercedes, s/n. 41012-Sevilla, Spain, Spain |
References:
[1] |
Focus issue edited by S. Flach and R. S. Mackay, Localization in nonlinear lattices, Physica D, 119 (1999), 1. |
[2] |
Focus issue edited by Yu S. Kivshar and S. Flach, Nonlinear localized modes: Physics and applications, Chaos, 13 (2003), 586. |
[3] |
Focus issue edited by T. Dauxois, R. S. Mackay and G. P. Tsironis, Condensed matter, dynamical systems and biophysics, Physica D, 216 (2006), 1. |
[4] |
A. Alvarez, F. R. Romero, J. F. R. Archilla, J. Cuevas and P. V. Larsen, Breather trapping and breather tansmission in a DNA model with an interface, Eur. Phys. J. B, 51 (2006), 119.
doi: doi:10.1140/epjb/e2006-00191-0. |
[5] |
A. Alvarez, F. R. Romero, J. Cuevas and J. F. R. Archilla, Discrete moving breather collisions in a Klein-Gordon chain of oscillators, Phys. Lett. A, 372 (2008), 1256.
doi: doi:10.1016/j.physleta.2007.09.035. |
[6] |
A. Alvarez, F. R. Romero, J. Cuevas and J. F. R. Archilla, Moving breather collisions in Klein-Gordon chains of oscillators, Eur. Phys. J. B, 70 (2009), 543.
doi: doi:10.1140/epjb/e2009-00256-6. |
[7] |
S. Aubry, Breathers in nonlinear lattices: Existence, linear stability and quantization, Physica D, 103 (1997), 201.
doi: doi:10.1016/S0167-2789(96)00261-8. |
[8] |
S. Aubry and T. Cretegny, Mobility and reactivity of discrete breathers, Physica D, 119 (1998), 34.
doi: doi:10.1016/S0167-2789(98)00062-1. |
[9] |
D. Campbell, J. Schonfeld and C. Wingate, Resonance structure in kink-antikink interactions in $\phi^4$ theory, Physica D, 9 (1983), 1.
doi: doi:10.1016/0167-2789(83)90289-0. |
[10] |
D. Chen, S. Aubry and G. P. Tsironis, Breather mobility in discrete $\varphi^4$ nonlinear lattices, Phys. Rev. Lett., 77 (1996), 4776.
doi: doi:10.1103/PhysRevLett.77.4776. |
[11] |
J. Cuevas, J. F. R. Archilla, Yu. B. Gaididei and F. R. Romero, Moving breathers in a DNA model with competing short and long range dispersive interactions, Physica D, 163 (2002), 106.
doi: doi:10.1016/S0167-2789(02)00351-2. |
[12] |
J. Cuevas and J. C. Eilbeck, Soliton collisions in a waveguide array with saturable nonlinearity, Phys. Lett. A, 358 (2006), 15.
doi: doi:10.1016/j.physleta.2006.04.095. |
[13] |
J. Cuevas, F. Palmero, J. F. R. Archilla and F. R. Romero, Moving breathers in a bent DNA-related model, Phys. Lett. A, 299 (2002), 221.
doi: doi:10.1016/S0375-9601(02)00731-4. |
[14] |
J. Cuevas, F. Palmero, J. F. R. Archilla and F. R. Romero, Moving discrete breathers in a Klein-Gordon chain with an impurity, J. Phys. A: Math. and Gen., 35 (2002), 10519.
doi: doi:10.1088/0305-4470/35/49/302. |
[15] |
T. Dauxois and M. Peyrard, Energy localization in nonlinear lattices, Phys. Rev. Lett., 70 (1993), 3935.
doi: doi:10.1103/PhysRevLett.70.3935. |
[16] |
T. Dauxois, M. Peyrard and C. R. Willis, Localized breather-like solutions in a discrete Klein-Gordon model and application to DNA, Physica D, 57 (1992), 267.
doi: doi:10.1016/0167-2789(92)90003-6. |
[17] |
S. Dmitriev, P. Kevrekidis and Y. Kivshar, Radiationless energy exchange in three-soliton collisions, Phys. Rev. E, 78 (2008), 046604.
doi: doi:10.1103/PhysRevE.78.046604. |
[18] |
Y. Doi, Energy exchange in collisions of intrinsic localized modes, Phys. Rev. E, 68 (2003), 066608.
doi: doi:10.1103/PhysRevE.68.066608. |
[19] |
S. Flach and C. R. Willis, Discrete breathers, Phys. Rep., 295 (1998), 181.
doi: doi:10.1016/S0370-1573(97)00068-9. |
[20] |
K. Forinash, T. Cretegny and M. Peyrard, Local modes and localization in amulticomponent nonlinear lattice, Phys. Rev. E, 55 (1997), 4740.
doi: doi:10.1103/PhysRevE.55.4740. |
[21] |
K. Forinash, M. Peyrard and B. A. Malomed, Interaction of discrete breathers with impurity modes, Phys. Rev. E, 49(1994), 3400.
doi: doi:10.1103/PhysRevE.49.3400. |
[22] |
P. G. Kevrekidis, K. Ø. Rasmussen and A. R. Bishop, The discrete nonlinear Schrödinger equation: A survey of recent results, Int. J. Mod. Phys. B, 15 (2001), 2833.
doi: doi:10.1142/S0217979201007105. |
[23] |
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.
doi: doi:10.1088/0951-7715/7/6/006. |
[24] |
J. L. Marín and S. Aubry, Breathers in nonlinear lattices: Numerical calculation from the anticontinuous limit, Nonlinearity, 9 (1996), 1501.
doi: doi:10.1088/0951-7715/9/6/007. |
[25] |
M. Meister and L. M. Floría, Bound states of breathers in the Frenkel-Kontorova model, Eur. Phys. J. B, 37 (2004), 213.
doi: doi:10.1140/epjb/e2004-00049-5. |
[26] |
I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed and D. J. Frantzeskakis, Soliton collisions in discrete nonlinear Schrödinger equation, Phys. Rev. E, 68 (2003), 046604.
doi: doi:10.1103/PhysRevE.68.046604. |
[27] |
M. Peyrard and A. R. Bishop, Statistical mechanics of a nonlinear model for DNA denaturation, Phys. Rev. Lett., 62 (1989), 2755.
doi: doi:10.1103/PhysRevLett.62.2755. |
[28] |
B. Sánchez-Rey, G. James, J. Cuevas and J. F. R. Archilla, Bright and dark breathers in Fermi-Pasta-Ulam lattices, Phys. Rev. B, 70 (2004), 014301.
doi: doi:10.1103/PhysRevB.70.014301. |
[29] |
M. Sanz-Serna and M. P. Calvo, "Numerical Hamiltonian Problems," Chapman and Hall, 1994. |
[30] |
A. J. Sievers and S. Takeno, Intrinsic localized modes in anharmonic crystals, Phys. Rev. Lett., 61 (1988), 970.
doi: doi:10.1103/PhysRevLett.61.970. |
show all references
References:
[1] |
Focus issue edited by S. Flach and R. S. Mackay, Localization in nonlinear lattices, Physica D, 119 (1999), 1. |
[2] |
Focus issue edited by Yu S. Kivshar and S. Flach, Nonlinear localized modes: Physics and applications, Chaos, 13 (2003), 586. |
[3] |
Focus issue edited by T. Dauxois, R. S. Mackay and G. P. Tsironis, Condensed matter, dynamical systems and biophysics, Physica D, 216 (2006), 1. |
[4] |
A. Alvarez, F. R. Romero, J. F. R. Archilla, J. Cuevas and P. V. Larsen, Breather trapping and breather tansmission in a DNA model with an interface, Eur. Phys. J. B, 51 (2006), 119.
doi: doi:10.1140/epjb/e2006-00191-0. |
[5] |
A. Alvarez, F. R. Romero, J. Cuevas and J. F. R. Archilla, Discrete moving breather collisions in a Klein-Gordon chain of oscillators, Phys. Lett. A, 372 (2008), 1256.
doi: doi:10.1016/j.physleta.2007.09.035. |
[6] |
A. Alvarez, F. R. Romero, J. Cuevas and J. F. R. Archilla, Moving breather collisions in Klein-Gordon chains of oscillators, Eur. Phys. J. B, 70 (2009), 543.
doi: doi:10.1140/epjb/e2009-00256-6. |
[7] |
S. Aubry, Breathers in nonlinear lattices: Existence, linear stability and quantization, Physica D, 103 (1997), 201.
doi: doi:10.1016/S0167-2789(96)00261-8. |
[8] |
S. Aubry and T. Cretegny, Mobility and reactivity of discrete breathers, Physica D, 119 (1998), 34.
doi: doi:10.1016/S0167-2789(98)00062-1. |
[9] |
D. Campbell, J. Schonfeld and C. Wingate, Resonance structure in kink-antikink interactions in $\phi^4$ theory, Physica D, 9 (1983), 1.
doi: doi:10.1016/0167-2789(83)90289-0. |
[10] |
D. Chen, S. Aubry and G. P. Tsironis, Breather mobility in discrete $\varphi^4$ nonlinear lattices, Phys. Rev. Lett., 77 (1996), 4776.
doi: doi:10.1103/PhysRevLett.77.4776. |
[11] |
J. Cuevas, J. F. R. Archilla, Yu. B. Gaididei and F. R. Romero, Moving breathers in a DNA model with competing short and long range dispersive interactions, Physica D, 163 (2002), 106.
doi: doi:10.1016/S0167-2789(02)00351-2. |
[12] |
J. Cuevas and J. C. Eilbeck, Soliton collisions in a waveguide array with saturable nonlinearity, Phys. Lett. A, 358 (2006), 15.
doi: doi:10.1016/j.physleta.2006.04.095. |
[13] |
J. Cuevas, F. Palmero, J. F. R. Archilla and F. R. Romero, Moving breathers in a bent DNA-related model, Phys. Lett. A, 299 (2002), 221.
doi: doi:10.1016/S0375-9601(02)00731-4. |
[14] |
J. Cuevas, F. Palmero, J. F. R. Archilla and F. R. Romero, Moving discrete breathers in a Klein-Gordon chain with an impurity, J. Phys. A: Math. and Gen., 35 (2002), 10519.
doi: doi:10.1088/0305-4470/35/49/302. |
[15] |
T. Dauxois and M. Peyrard, Energy localization in nonlinear lattices, Phys. Rev. Lett., 70 (1993), 3935.
doi: doi:10.1103/PhysRevLett.70.3935. |
[16] |
T. Dauxois, M. Peyrard and C. R. Willis, Localized breather-like solutions in a discrete Klein-Gordon model and application to DNA, Physica D, 57 (1992), 267.
doi: doi:10.1016/0167-2789(92)90003-6. |
[17] |
S. Dmitriev, P. Kevrekidis and Y. Kivshar, Radiationless energy exchange in three-soliton collisions, Phys. Rev. E, 78 (2008), 046604.
doi: doi:10.1103/PhysRevE.78.046604. |
[18] |
Y. Doi, Energy exchange in collisions of intrinsic localized modes, Phys. Rev. E, 68 (2003), 066608.
doi: doi:10.1103/PhysRevE.68.066608. |
[19] |
S. Flach and C. R. Willis, Discrete breathers, Phys. Rep., 295 (1998), 181.
doi: doi:10.1016/S0370-1573(97)00068-9. |
[20] |
K. Forinash, T. Cretegny and M. Peyrard, Local modes and localization in amulticomponent nonlinear lattice, Phys. Rev. E, 55 (1997), 4740.
doi: doi:10.1103/PhysRevE.55.4740. |
[21] |
K. Forinash, M. Peyrard and B. A. Malomed, Interaction of discrete breathers with impurity modes, Phys. Rev. E, 49(1994), 3400.
doi: doi:10.1103/PhysRevE.49.3400. |
[22] |
P. G. Kevrekidis, K. Ø. Rasmussen and A. R. Bishop, The discrete nonlinear Schrödinger equation: A survey of recent results, Int. J. Mod. Phys. B, 15 (2001), 2833.
doi: doi:10.1142/S0217979201007105. |
[23] |
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.
doi: doi:10.1088/0951-7715/7/6/006. |
[24] |
J. L. Marín and S. Aubry, Breathers in nonlinear lattices: Numerical calculation from the anticontinuous limit, Nonlinearity, 9 (1996), 1501.
doi: doi:10.1088/0951-7715/9/6/007. |
[25] |
M. Meister and L. M. Floría, Bound states of breathers in the Frenkel-Kontorova model, Eur. Phys. J. B, 37 (2004), 213.
doi: doi:10.1140/epjb/e2004-00049-5. |
[26] |
I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed and D. J. Frantzeskakis, Soliton collisions in discrete nonlinear Schrödinger equation, Phys. Rev. E, 68 (2003), 046604.
doi: doi:10.1103/PhysRevE.68.046604. |
[27] |
M. Peyrard and A. R. Bishop, Statistical mechanics of a nonlinear model for DNA denaturation, Phys. Rev. Lett., 62 (1989), 2755.
doi: doi:10.1103/PhysRevLett.62.2755. |
[28] |
B. Sánchez-Rey, G. James, J. Cuevas and J. F. R. Archilla, Bright and dark breathers in Fermi-Pasta-Ulam lattices, Phys. Rev. B, 70 (2004), 014301.
doi: doi:10.1103/PhysRevB.70.014301. |
[29] |
M. Sanz-Serna and M. P. Calvo, "Numerical Hamiltonian Problems," Chapman and Hall, 1994. |
[30] |
A. J. Sievers and S. Takeno, Intrinsic localized modes in anharmonic crystals, Phys. Rev. Lett., 61 (1988), 970.
doi: doi:10.1103/PhysRevLett.61.970. |
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