Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2005-02-28
Phys. Rev. E 72, 056607 (2005)
Nonlinear Sciences
Pattern Formation and Solitons
5 pages, 4 figures, revised version, published in PRE
Scientific paper
10.1103/PhysRevE.72.056607
Discrete breathers with purely anharmonic short-range interaction potentials localize super-exponentially becoming compact-like. We analyze their spatial localization properties and their dynamical stability. Several branches of solutions are identified. One of them connects to the well-known Page and Sievers-Takeno lattice modes, another one connects with the compacton solutions of Rosenau. The absence of linear dispersion allows for extremely long-lived time-quasiperiodic localized excitations. Adding long-range anharmonic interactions leads to an extreme case of competition between length scales defining the spatial breather localization. We show that short- and long-range interaction terms competition results in the appearance of several characteristic cross-over lengths and essentially breaks the concept of compactness of the corresponding discrete breathers.
Flach Sergej
Gorbach Andrey V.
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