Multibreathers and homoclinic orbits in 1-dimensional nonlinear lattices

被引:57
作者
Bountis, T [1 ]
Capel, HW
Kollmann, M
Ross, JC
Bergamin, JM
van der Weele, JP
机构
[1] Univ Patras, Dept Math, Patras 26500, Greece
[2] Univ Patras, Ctr Res & Applicat Nonlinear Syst, Patras 26500, Greece
[3] Univ Amsterdam, Inst Theoret Phys, NL-1018 XE Amsterdam, Netherlands
[4] Univ Twente, Theoret Phys Grp, NL-7500 AE Enschede, Netherlands
关键词
D O I
10.1016/S0375-9601(00)00100-6
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Spatially localized, time-periodic excitations, known as discrete breathers, have been found to occur in a wide variety of 1-dimensional (1-D) lattices of nonlinear oscillators with nearest-neighbour coupling. Eliminating the time-dependence from the differential-difference equations of motion, and taking into account only the N largest Fourier modes, we view these solutions as orbits of a (non-integrable) 2N-D map. For breathers to occur, the trivial rest state of the lattice must be a hyperbolic fixed point of the map, with an N-D stable and an N-D unstable manifold. The breathers and multibreathers (with one and more spatial oscillations respectively) are then directly related to the intersections of these manifolds, and hence to homoclinic orbits of the 2 N-D map. This is explicitly shown here on a discretized nonlinear Schrodinger equation with only one Fourier mode (N= 1), represented by a 2-D map. We then construct the 2N-D map for an array of nonlinear oscillators. with nearest neighbour coupling and a quartic on-site potential, and demonstrate how a one-Fourier-mode representation (via 2-D map) can be used to provide remarkably accurate initial conditions for the breather and multibreather solutions of the system. (C) 2000 Published by Elsevier Science B.V. All rights reserved.
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页码:50 / 60
页数:11
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