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Analysis of the response of damped and parametrically driven, strongly anharmonic Klein-Gordon chain - Part 1: Phase locked traveling breathers

Author

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  • Gzal, M.
  • Kislovsky, V.
  • Hasan, M.A.
  • Starosvetsky, Y.

Abstract

In the present study, we analyze a special type of phase-locked, compact-like, moving breather solution emerging in damped, strongly nonlinear Klein-Gordon chains subjected to parametric traveling-wave excitation. Given the strongly anharmonic nature of the system under consideration, multi-scale analysis of various nonlinear wave phenomena emerging in this model becomes a highly nontrivial task. In this work, we derive the two distinct analytical approaches that enable the analytical characterization of moving, damped-driven breather solutions. As is evident from the results of the present study, the moving breather solutions forming in the damped-driven lattice under consideration are unidirectional. Moreover, their dynamics is fully controlled by the parameters of the applied, traveling wave-like, parametric excitation. These special properties of strongly localized solutions provide the new means for active spatial-temporal control of these strongly localized wave structures.

Suggested Citation

  • Gzal, M. & Kislovsky, V. & Hasan, M.A. & Starosvetsky, Y., 2023. "Analysis of the response of damped and parametrically driven, strongly anharmonic Klein-Gordon chain - Part 1: Phase locked traveling breathers," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s096007792201205x
    DOI: 10.1016/j.chaos.2022.113026
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    Cited by:

    1. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Alquhayz, Hani & Abdalla, Manal Z.M. & Alhagyan, Mohammed & Gargouri, Ameni & Shoaib, Muhammad, 2023. "Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    2. Jin, Qiduo & Yuan, Fuh-Gwo & Ren, Yiru, 2023. "Auto-parametric resonance of flexible viscoelastic beams under interaction between longitudinal and transverse modes," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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