Abstract.
Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam (FPU)-like lattices were recently generalized to the case of dispersive long-range interactions (LRI) of the Kac-Baker form. The variance of the soliton position shows a stronger than linear time-dependence (superdiffusion) as found earlier for lattice solitons on FPU chains with nearest-neighbour interactions (NNI). Since the superdiffusion seems to be generic for nontopological solitons, we want to illuminate the role of the soliton shape on the superdiffusive mechanism. Therefore, we concentrate on an FPU-like lattice with a certain class of power-law long-range interactions where the solitons have algebraic tails instead of the exponential tails in the case of FPU-type interactions (with or without Kac-Baker LRI).Despite of structurally similar Langevin equations which hold for the soliton position and width of the two soliton types, the algebraic solitons reach the superdiffusive long-time limit with a characteristic t3/2 time-dependence much faster than exponential solitons. The soliton shape determines the diffusion constant in the long-time limit that is approximately a factor of π smaller for algebraic solitons. Our results appear to be generic for nonlinear excitaitons in FPU-chains, because the same superdiffusive time-dependence was also observed in simulations with discrete breathers.
Similar content being viewed by others
References
A.C. Scott, Nonlinear Science (University Press Oxford, 1999)
The Encyclopedia of Nonlinear Science, edited by A.C. Scott (Routledge, New York, 2005)
T. Dauxois, M. Peyrard, Physics of Solitons (Cambridge University Press, 2005)
A.S. Davydov, Solitons in Molecular Systems (Reidel, Dotrecht, 1985)
A.C. Scott, Physics Reports 217, 1 (1992)
M. Peyrard, Nonlinearity 17, R1 (2004)
L.V. Yakushevich, J. Biosci. 26, 305 (2001)
J. Edler, P. Hamm, A.C. Scott, Phys. Rev. Lett. 88, 067403 (2002)
L. Cruzeiro-Hansson, S. Takeno, Phys. Rev. E, 56, 894 (1997)
C.H. Choi, G. Kalosakas, K.Ø. Rasmussen, M. Hiromura, A.R. Bishop, A. Usheva, Nucleic Acids Res. 32, 1584
Y.B. Gaididei, N. Flytzanis, A. Neuper, F.G. Mertens, Physica D 107, 83
S. Flach, Phys. Rev. E 58, R4116 (1998)
P.L. Christiansen, Y.B. Gaididei, F.G. Mertens, S.F. Mingaleev, Eur. Phys. J. B 19, 545
S.F. Mingaleev, P.L. Christiansen, Yu.B. Gaididei, M. Johansson, K.Ø. Rasmussen, J. Biol. Phys. 25, 41 (1999)
O.M. Braun, Yu. S. Kivshar, Physics Reports 306, 1 (1998)
D. Bonart, Phys. Lett. A 231, 201 (1997)
T. Rössler, J.B. Page, Phys. Rev. B 62, 11460 (2000)
L. Cruzeiro-Hansson, Phys. Lett. A 249, 465 (1998)
K.Ø. Rasmussen, P.L. Christiansen, M. Johansson, Yu. B. Gaididei, S.F. Mingaleev, Physica D 113, 134 (1998)
Dynamics and Thermodynamics of Systems with Long-Range Interactions, edited by D. Ruffo, A. Wilkens Lecture Notes in Physics 602 (Springer, 2002)
C. Brunhuber, F.G. Mertens, Y. Gaididei, Phys. Rev. E 73, 016614 (2006)
S.F. Mingaleev, Y.B. Gaididei, F.G. Mertens, Phys. Rev. E 61, R1044
C. Brunhuber, F.G. Mertens, Y. Gaididei, Phys. Rev. E 75, 036615 (2007)
E. Arévalo, F.G. Mertens, Y. Gaididei, A.R. Bishop, Phys. Rev. E 67, 016610 (2003)
R. Reigada, A. Sarmiento, K. Lindenberg, Phys. Rev. E 64, 066608 (2001)
S. Mingaleev, Y. Gaididei, F.G. Mertens, Phys. Rev. E 58, 3833 (1998)
A.S. Cârstea, D. Grecu, Anca Vişinescu, Phys. Lett. A, 246, 82 (1998)
Y. Ishimori, Prog. Theor. Phys. 68, 402 (1982)
E. Arévalo, F.G. Mertens, A.R. Bishop, Eur. Phys. J. B 27 63 (2002)
L.A. Ostrovsky, E.N. Pelinovsky, Sov. Phys. Dokl. 15, 1097 (1971)
A. Jeffrey, T. Kawahara, Asymptotic Methods in Nonlinear Wave Theory (Pitman, London, 1982)
C. Brunhuber, F.G. Mertens, Y. Gaididei, Eur. Phys. J. B 42, 103 (2004)
V. Konotop, L. Vázquez, Nonlinear Random Waves (World Scientific, Singapore, 1994)
C.W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, New York-Heidelberg-Berlin, 1983)
F.G. Mertens, E. Arévalo, A.R. Bishop, Phys. Rev. E 72, 036617 (2005)
E. Arévalo, Dissertation (Universität Bayreuth, 2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Brunhuber, C., Mertens, F. & Gaididei, Y. Long-range effects on superdiffusive algebraic solitons in anharmonic chains. Eur. Phys. J. B 57, 57–65 (2007). https://doi.org/10.1140/epjb/e2007-00150-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2007-00150-3