Breatherlike impurity modes in discrete nonlinear lattices

D. Hennig; K. Ø. Rasmussen; G. P. Tsironis; H. Gabriel

doi:10.1103/PhysRevE.52.R4628

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Breatherlike impurity modes in discrete nonlinear lattices

D. Hennig, K. Ø. Rasmussen, G. P. Tsironis, and H. Gabriel

Fachbereich Physik, Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
Institute of Mathematical Modelling, Technical University of Denmark, 2800 Lyngby, Denmark
Physics Department and Research Center of Crete, University of Crete, P.O Box 1527, Heraklion 71110, Crete, Greece
Center for Nonlinear Science and Department of Physics, University of North Texas, Denton, Texas 76203

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Phys. Rev. E 52, R4628(R) – Published 1 November, 1995

DOI: https://doi.org/10.1103/PhysRevE.52.R4628

Abstract

We investigate the properties of a disordered generalized discrete nonlinear Schrödinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant breather states in the vicinity of the impurities. We analyze the properties of these breathers analytically and numerically.

References (19)

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[c1] Disorder and Nonlinearity, edited by A.R. Bishop, D.K. Campbell, and S. Pnevmatikos (Springer-Verlag, New York, 1989).

[c2] Disorder with Nonlinearity, edited by F. Abdullaev, A.R. Bishop, and S. Pnevmatikos (Springer-Verlag, Berlin, 1992).

[c3] S. Takeno and S. Homma, J. Phys. Soc. Jpn. 60, 731 (1991), 62, 835 (1993); A.J. Sievers and S. Takeno, Phys. Rev. Lett. 61, 970 (1988); S. Takeno and K. Hori, J. Phys. Soc. Jpn. 60, 947 (1991); S. Takeno, ibid. 61, 2821 (1992); S.R. Bickham, S.A. Kiselev and A.J. Sievers, Phys. Rev. B 47, 14t206 (1993); J.B. Page, ibid. 41, 7835 (1990); K.W. Sandudsky, J.B. Page and K.E. Schmidt, ibid. 46, 6161 (1992).

[c4] D. L. Shepelyansky, Phys. Rev. Lett. 70, 1787 (1993).

[c5] M. I. Molina and G. P. Tsironis, Phys. Rev. Lett. 73, 464 (1994).

[c6] E.N. Economou, Green's Functions in Quantum Physics, Springer Series in Solid State Sciences Vol. 7 (Springer-Verlag, Berlin, 1979).

[c7] M.I. Molina and G.P. Tsironis, Phys. Rev. B 47, 15t330 (1993).

[c8] D. Chen, M. Molina and G.P. Tsironis, J. Phys. Cond. Matter 5, 8689 (1993).

[c9] G.P. Tsironis, M.I. Molina and D. Hennig, Phys. Rev. E 50, 2365 (1994).

[c10] D. Dunlap, V.M. Kenkre and P. Reineker, Phys. Rev. B 47, 14t842 (1993).

[c11] M. Salerno, Phys. Rev. A 46, 6856 (1992).

[c12] D. Cai, A.R. Bishop and N. Grønbech-Jensen, Phys. Rev. Lett. 72, 591 (1994).

[c13] D. Cai, A.R. Bishop, N. Grønbech-Jensen and M. Salerno, Phys. Rev. Lett. 74, 1186 (1995).

[c14] Yu.S. Kivshar and M. Salerno, Phys. Rev. E 49, 3543 (1994).

[c15] D. Hennig, N.G. Sun, H. Gabriel and G.P. Tsironis, Phys. Rev. E 52, 255 (1995).

[c16] M.J. Ablowitz and J.F. Ladik, J. Math. Phys. 17, 1011 (1976).

[c17] J.C. Eilbeck, P.S. Lomdahl and A.C. Scott, Physica 16, 318 (1985).

[c18] S. Aubry, Physica D71, 196 (1994).

[c19] R.S. MacKay and S. Aubry, Nonlinearity 7, 1623 (1994).

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Breatherlike impurity modes in discrete nonlinear lattices

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