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Nonlinear parametric instability in double-well lattices.

J Riedel1, B A Malomed, E Majerníková

  • 1Department of Theoretical Physics, Palacký University, Tr. 17, Listopadu 50, 77207 Olomouc, Czech Republic.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
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Researchers predict and confirm a nonlinear resonant instability in dynamical lattices. This instability, with an anomalous power index, transitions the lattice into a chaotic dynamical state.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Lattice dynamics

Background:

  • Dynamical lattices with harmonic intersite coupling and onsite nonlinearity are crucial in various physics domains.
  • Understanding instabilities in these systems is key to predicting their behavior.

Purpose of the Study:

  • To predict and investigate the possibility of a nonlinear resonant instability in uniform oscillations within dynamical lattices.
  • To characterize the nature of this instability and its impact on lattice dynamics.

Main Methods:

  • Theoretical prediction of nonlinear resonant instability.
  • Numerical simulations of a lattice model featuring a double-well onsite anharmonic potential.

Main Results:

Related Experiment Videos

  • Confirmation of the existence of a nonlinear instability.
  • Observation of an anomalous power index (approximately 1.57) for the instability.
  • The anomalous index is intermediate between linear (1) and quadratic (2) instability values.

    • Conclusions:

    • The nonlinear resonant instability arises from a competition between resonant quadratic and nonresonant linear instabilities.
    • This instability triggers a transition of the lattice into a chaotic dynamical state.