Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2025
• Автори: Vakhnenko, Oleksiy O., Vakhnenko, Vyacheslav O.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2025
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/214195
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice. Oleksiy O. Vakhnenko and Vyacheslav O. Vakhnenko. SIGMA 21 (2025), 089, 17 pages

Bearing in mind the potential physical applicability of multicomponent completely integrable nonlinear dynamical models on quasi-one-dimensional lattices, we have developed the novel twelve-component and six-component semi-discrete nonlinear integrable systems in the framework of the semi-discrete Ablowitz-Kaup-Newell-Segur scheme. The set of lowest local conservation laws found by the generalized direct recurrent technique was shown to be an indispensable constructive tool in the reduction procedure from the prototype to actual field variables. Two types of admissible symmetries for the twelve-component system and one type of symmetry for the six-component system have been established. The mathematical structure of the total local current was shown to support the charge transportation only by four of six subsystems incorporated into the twelve-component system under study. The twelve-component system is able to model the actions of external parametric drive and external uniform magnetic field via time dependencies and phase factors of coupling parameters.