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Area of Science:

  • Nonlinear physics
  • Condensed matter physics
  • Lattice dynamics

Background:

  • Investigates the diamond-chain model, a fundamental structure in lattice dynamics.
  • Focuses on systems with on-site cubic nonlinearity and inter-chain linear mixing.
  • Examines the behavior of wave propagation and localization in discrete systems.

Purpose of the Study:

  • To systematically analyze various stationary and non-stationary modes in single and double nonlinear diamond-chain lattices.
  • To find exact solutions for compact localized states (CLSs) and investigate their stability.
  • To identify the existence and stability regions for different types of localized and extended states.

Main Methods:

  • Analytical methods for solving nonlinear equations and identifying stationary states.
  • Exact solutions for compact localized states (CLSs) in nonlinear infinite chains.
  • Numerical calculations and variational approximation for stability analysis and characterization of solitons.

Main Results:

  • All stationary states (antisymmetric, symmetric, asymmetric) were found for a single nonlinear cell, including subcritical symmetry-breaking bifurcations.
  • Exact forms for compact localized states (CLSs) were derived, extending solutions from linear chains, with a non-trivial stability boundary identified.
  • Existence and stability areas for extended states and symmetric/asymmetric solitons were mapped using numerical and variational methods.

Conclusions:

  • The study provides a comprehensive understanding of diverse wave phenomena in nonlinear diamond-chain lattices.
  • Exact solutions and stability analyses offer crucial insights into the behavior of localized and extended modes.
  • The linear double diamond chain exhibits split flatbands, indicating unique spectral properties.