Numerical approximation of breathers in lattices with nearest-neighbor interactions

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 2 2, 2003, Pages 267031-2670310

  Bergamin, J M ^a  

^a UNIVERSITY OF PATRAS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; NONLINEAR SYSTEMS; VECTORS; WAVEGUIDES;

BREATHERS;

CRYSTAL LATTICES;

EID: 0037719937     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

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16. See, e.g., Ref. [1]; J.B. Page, Phys. Rev. B 41, 7835 (1990); S.R. Bickham and A.J. Sievers, ibid. 43, 2339 (1991); S.R. Bickham, A.J. Sievers, and S. Takeno, ibid. 45, 10 344 (1992); K.W. Sandusky, J.B. Page, and K..E. Schmidt, ibid. 46, 6161 (1992); V.M. Burlakov, S.A. Kiselev, and V.I. Rupasov, Phys. Lett. A 147, 130 (1990); S. Takeno, J. Phys. Soc. Jpn. 59, 1571 (1990); S. Takeno, ibid. 59, 3861 (1990); S. Takeno and K. Hori, ibid. 59, 3037 (1990); K. Hori and S. Takeno, ibid. 61, 4263 (1992).
17. See, e.g., Ref. [1]; J.B. Page, Phys. Rev. B 41, 7835 (1990); S.R. Bickham and A.J. Sievers, ibid. 43, 2339 (1991); S.R. Bickham, A.J. Sievers, and S. Takeno, ibid. 45, 10 344 (1992); K.W. Sandusky, J.B. Page, and K..E. Schmidt, ibid. 46, 6161 (1992); V.M. Burlakov, S.A. Kiselev, and V.I. Rupasov, Phys. Lett. A 147, 130 (1990); S. Takeno, J. Phys. Soc. Jpn. 59, 1571 (1990); S. Takeno, ibid. 59, 3861 (1990); S. Takeno and K. Hori, ibid. 59, 3037 (1990); K. Hori and S. Takeno, ibid. 61, 4263 (1992).
18. See, e.g., Ref. [1]; J.B. Page, Phys. Rev. B 41, 7835 (1990); S.R. Bickham and A.J. Sievers, ibid. 43, 2339 (1991); S.R. Bickham, A.J. Sievers, and S. Takeno, ibid. 45, 10 344 (1992); K.W. Sandusky, J.B. Page, and K..E. Schmidt, ibid. 46, 6161 (1992); V.M. Burlakov, S.A. Kiselev, and V.I. Rupasov, Phys. Lett. A 147, 130 (1990); S. Takeno, J. Phys. Soc. Jpn. 59, 1571 (1990); S. Takeno, ibid. 59, 3861 (1990); S. Takeno and K. Hori, ibid. 59, 3037 (1990); K. Hori and S. Takeno, ibid. 61, 4263 (1992).
19. See, e.g., Ref. [1]; J.B. Page, Phys. Rev. B 41, 7835 (1990); S.R. Bickham and A.J. Sievers, ibid. 43, 2339 (1991); S.R. Bickham, A.J. Sievers, and S. Takeno, ibid. 45, 10 344 (1992); K.W. Sandusky, J.B. Page, and K..E. Schmidt, ibid. 46, 6161 (1992); V.M. Burlakov, S.A. Kiselev, and V.I. Rupasov, Phys. Lett. A 147, 130 (1990); S. Takeno, J. Phys. Soc. Jpn. 59, 1571 (1990); S. Takeno, ibid. 59, 3861 (1990); S. Takeno and K. Hori, ibid. 59, 3037 (1990); K. Hori and S. Takeno, ibid. 61, 4263 (1992).
20. See, e.g., Ref. [1]; J.B. Page, Phys. Rev. B 41, 7835 (1990); S.R. Bickham and A.J. Sievers, ibid. 43, 2339 (1991); S.R. Bickham, A.J. Sievers, and S. Takeno, ibid. 45, 10 344 (1992); K.W. Sandusky, J.B. Page, and K..E. Schmidt, ibid. 46, 6161 (1992); V.M. Burlakov, S.A. Kiselev, and V.I. Rupasov, Phys. Lett. A 147, 130 (1990); S. Takeno, J. Phys. Soc. Jpn. 59, 1571 (1990); S. Takeno, ibid. 59, 3861 (1990); S. Takeno and K. Hori, ibid. 59, 3037 (1990); K. Hori and S. Takeno, ibid. 61, 4263 (1992).
21. See, e.g., Ref. [1]; J.B. Page, Phys. Rev. B 41, 7835 (1990); S.R. Bickham and A.J. Sievers, ibid. 43, 2339 (1991); S.R. Bickham, A.J. Sievers, and S. Takeno, ibid. 45, 10 344 (1992); K.W. Sandusky, J.B. Page, and K..E. Schmidt, ibid. 46, 6161 (1992); V.M. Burlakov, S.A. Kiselev, and V.I. Rupasov, Phys. Lett. A 147, 130 (1990); S. Takeno, J. Phys. Soc. Jpn. 59, 1571 (1990); S. Takeno, ibid. 59, 3861 (1990); S. Takeno and K. Hori, ibid. 59, 3037 (1990); K. Hori and S. Takeno, ibid. 61, 4263 (1992).
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23. For example, S. Takeno and K. Hori, J. Phys. Soc. Jpn. 60, 847 (1991); S. Takeno, ibid. 61, 2821 (1992); Y.S. Kivshar, Phys. Lett. A 173, 172 (1993); S. Flach, Phys. Rev. E 50, 3134 (1994); S. Flach, ibid. 51, 1503 (1995); S. Flach, ibid. 51, 3579 (1995); O. Bang and M. Peyrard, ibid. 53, 4143 (1996); J.L. Marin, S. Aubry, and L.M. Floria, Physica D 113, 283 (1998); J.F.R. Archilla, R.S. MacKay, and J.L. Marin, ibid. 134, 406 (1999).
24. For example, S. Takeno and K. Hori, J. Phys. Soc. Jpn. 60, 847 (1991); S. Takeno, ibid. 61, 2821 (1992); Y.S. Kivshar, Phys. Lett. A 173, 172 (1993); S. Flach, Phys. Rev. E 50, 3134 (1994); S. Flach, ibid. 51, 1503 (1995); S. Flach, ibid. 51, 3579 (1995); O. Bang and M. Peyrard, ibid. 53, 4143 (1996); J.L. Marin, S. Aubry, and L.M. Floria, Physica D 113, 283 (1998); J.F.R. Archilla, R.S. MacKay, and J.L. Marin, ibid. 134, 406 (1999).
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28. For example, S. Takeno and K. Hori, J. Phys. Soc. Jpn. 60, 847 (1991); S. Takeno, ibid. 61, 2821 (1992); Y.S. Kivshar, Phys. Lett. A 173, 172 (1993); S. Flach, Phys. Rev. E 50, 3134 (1994); S. Flach, ibid. 51, 1503 (1995); S. Flach, ibid. 51, 3579 (1995); O. Bang and M. Peyrard, ibid. 53, 4143 (1996); J.L. Marin, S. Aubry, and L.M. Floria, Physica D 113, 283 (1998); J.F.R. Archilla, R.S. MacKay, and J.L. Marin, ibid. 134, 406 (1999).
29. For example, S. Takeno and K. Hori, J. Phys. Soc. Jpn. 60, 847 (1991); S. Takeno, ibid. 61, 2821 (1992); Y.S. Kivshar, Phys. Lett. A 173, 172 (1993); S. Flach, Phys. Rev. E 50, 3134 (1994); S. Flach, ibid. 51, 1503 (1995); S. Flach, ibid. 51, 3579 (1995); O. Bang and M. Peyrard, ibid. 53, 4143 (1996); J.L. Marin, S. Aubry, and L.M. Floria, Physica D 113, 283 (1998); J.F.R. Archilla, R.S. MacKay, and J.L. Marin, ibid. 134, 406 (1999).
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31. For example, S. Takeno and K. Hori, J. Phys. Soc. Jpn. 60, 847 (1991); S. Takeno, ibid. 61, 2821 (1992); Y.S. Kivshar, Phys. Lett. A 173, 172 (1993); S. Flach, Phys. Rev. E 50, 3134 (1994); S. Flach, ibid. 51, 1503 (1995); S. Flach, ibid. 51, 3579 (1995); O. Bang and M. Peyrard, ibid. 53, 4143 (1996); J.L. Marin, S. Aubry, and L.M. Floria, Physica D 113, 283 (1998); J.F.R. Archilla, R.S. MacKay, and J.L. Marin, ibid. 134, 406 (1999).
32. G.P. Tsironis, J. Phys. A 35, 951 (2002).
33. -6.
34. J.M. Bergamin, T. Bountis, and C. Jung, J. Phys. A 33, 8059 (2000).
35. J.M. Bergamin, T. Bountis, and M.N. Vrahatis, Nonlinearity 15, 1603 (2002).
36. For some other numerical approximations to breathers in two-dimensional lattices see, e.g., V.M. Burlakov, S.A. Kiselev, and V.N. Pyrkov, Phys. Rev. B 42, 4921 (1990); S. Flach, K. Kladko, and C.R. Willis, Phys. Rev. E 50, 2293 (1994).
37. For some other numerical approximations to breathers in two-dimensional lattices see, e.g., V.M. Burlakov, S.A. Kiselev, and V.N. Pyrkov, Phys. Rev. B 42, 4921 (1990); S. Flach, K. Kladko, and C.R. Willis, Phys. Rev. E 50, 2293 (1994).
38. W.-J. Beyn and J.-M. Kleinkauf, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 34, 1207 (1997); W.-J. Beyn and J.-M. Kleinkauf, Numer. Algorithms 14, 25 (1997).
39. W.-J. Beyn and J.-M. Kleinkauf, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 34, 1207 (1997); W.-J. Beyn and J.-M. Kleinkauf, Numer. Algorithms 14, 25 (1997).