Open AccessCoupled Nonlinear Dynamics in the Three-Mode Integrable System on a Regular Chain
Author(s) -
Oleksiy O. Vakhnenko
Publication year - 2021
Publication title -
ukrainian journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.213
H-Index - 17
eISSN - 2071-0194
pISSN - 2071-0186
DOI - 10.15407/ujpe66.7.601
Subject(s) - integrable system , nonlinear system , hamiltonian (control theory) , lax pair , curvature , dynamical systems theory , hamiltonian system , poisson bracket , eigenvalues and eigenvectors , operator (biology) , hamiltonian mechanics , lattice (music) , physics , mathematics , classical mechanics , pure mathematics , mathematical physics , quantum mechanics , geometry , mathematical optimization , biochemistry , chemistry , repressor , lie algebra , transcription factor , acoustics , phase space , gene
The article suggests the nonlinear lattice system of three dynamical subsystems coupled both in their potential and kinetic parts. Due to its essentially multicomponent structure the system is capable to model nonlinear dynamical excitations on regular quasi-one-dimensional lattices of various physical origins. The system admits a clear Hamiltonian formulation with the standard Poisson structure. The alternative Lagrangian formulation of system’s dynamics is also presented. The set of dynamical equations is integrable in the Lax sense, inasmuch as it possesses a zero-curvature representation. Though the relevant auxiliary linear problem involves a spectral third-order operator, we have managed to develop an appropriate two-fold Darboux–Backlund dressing technique allowing one to generate the nontrivial crop solution embracing all three coupled subsystems in a rather unusual way.