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According to the law of conservation of energy, any transition between kinetic and potential energy conserves the total energy of the system. Hence, the work done by a conservative force is completely reversible. It is path independent, which means that we can start and stop at any two points in the transition, and the total energy of the system (kinetic plus potential energy at these points) will remain conserved. This is characteristic of a conservative force. Some important examples of...
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Conservative and PT-symmetric compactons in waveguide networks.

A V Yulin, V V Konotop

    Optics Letters
    |December 11, 2013
    PubMed
    Summary

    Stable discrete compactons were discovered in waveguide arrays across linear and nonlinear models. These compactons, arising from field interference, exhibit unique properties in parity-time (PT)-symmetric systems.

    Area of Science:

    • Optics and Photonics
    • Nonlinear Physics
    • Waveguide Arrays

    Background:

    • Discrete compactons are localized nonlinear waves that exhibit finite energy and spatial localization.
    • Waveguide arrays provide a platform for studying discrete light propagation and nonlinear phenomena.
    • Parity-time (PT)-symmetric systems offer unique possibilities for controlling wave propagation with balanced gain and loss.

    Purpose of the Study:

    • To investigate the existence and stability of discrete compactons in interconnected three-line waveguide arrays.
    • To explore the behavior of these compactons in both conservative and parity-time (PT)-symmetric models.
    • To analyze the role of field interference and complex coupling in compacton formation and stability.

    Main Methods:

    • Analytical and numerical methods were employed to study compacton solutions.

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  • Linear stability analysis was performed to assess the stability of the obtained compactons.
  • The influence of gain, loss, and complex coupling in PT-symmetric systems was investigated.

    • Main Results:

    • Stable discrete compactons were found in both linear and nonlinear regimes for conservative and PT-symmetric waveguide arrays.
    • Compacton formation is attributed to field interference, leading to zero energy in the middle waveguide.
    • PT-symmetric compactons require specific conditions of gain, loss, and complex coupling.
    • The study revealed that compacton branches can cross with those of dissipative solitons, leading to unusual bifurcations.

    Conclusions:

    • Discrete compactons are robust phenomena in waveguide arrays, existing in various physical regimes.
    • PT-symmetry introduces novel mechanisms for compacton control and stability.
    • The observed bifurcations offer new insights into the dynamics of nonlinear waves in engineered structures.