Зв’язана нелінійна динаміка тримодової інтеґровної системи на регулярному ланцюжку

• Main Author: Vakhnenko, O.O.
• Format: Article
• Language: English
• Published: Publishing house "Academperiodika" 2021
• Subjects: нелiнiйнi теорiї та моделi; ангармонiйнi ґратковi моди; iнтеґровнi системи; Лаґранжова та Гамiльтонова динамiки; метод одягання Дарбу–Беклунда; симетрiя та закони збереження; нелiнiйний хвильовий пакет; English; nonlinear theories and models; anharmonic lattice modes; integrable systems; Lagrangian and Hamiltonian dynamics; Darboux–B¨acklund dressing method; symmetry and conservation laws; nonlinear wave packet; 11.10.Lm; 63.20.Ry; 02.30.Ik; 45.20.Jj; 02.30.Zz; 11.30.-j; 05.45.Yv
• Online Access: https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2020217

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.