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Nonlinear parametric instability in double-well lattices

Jaroslav Riedel·Eva Majernikova·Boris A. Malomed
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Abstract

A possibility of a nonlinear resonant instability of uniform oscillations in dynamical lattices with harmonic intersite coupling and onsite nonlinearity is predicted. Numerical simulations of a lattice with a double-well onsite anharmonic potential confirm the existence of the nonlinear instability with an anomalous value of the corresponding power index, 1.57, which is intermediate between the values 1 and 2 characterizing the linear and nonlinear (quadratic) instabilities. The anomalous power index may be a result of competition between the resonant quadratic instability and nonresonant linear instabilities. The observed instability triggers transition of the lattice into a chaotic dynamical state.

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Jaroslav Riedel, Eva Majernikova, Boris A. Malomed. 2001-06-17. Nonlinear parametric instability in double-well lattices. https://doi.org/10.1103/physreve.64.037602

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