BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:Canonization-based symmetry breaking in an integrable four-compone nt nonlinear dynamical system on a quasi-one-dimensional lattice with back ground-controlled intersite coupling DTSTART;VALUE=DATE-TIME:20260924T094000Z DTEND;VALUE=DATE-TIME:20260924T100000Z DTSTAMP;VALUE=DATE-TIME:20260914T040429Z UID:indico-contribution-504@indico.bitp.kiev.ua DESCRIPTION:Speakers: Vakhnenko Oleksiy O. (Bogolyubov Institute for Theor etical Physics)\nEleven years ago we developed the four-component nonlinea r integrable dynamical system on a ribbon of two-leg triangular lattice wi th the common coherent and uncommon background-controlled intersite coupli ngs [1\, 2]. The system can be classified as a sort of semi-discrete nonli near Schrödinger system. It characterized by four basic (independent) fie lds on zero background and two concomitant (dependent) fields on nonzero b ackground. Due to nonzero background values of concomitant fields the enti re Poisson structure of semi-discrete nonlinear system acquires essentiall y nonstandard form veiling the true physical interpretation of basic field s. Looking for a prospective physical applications of suggested semi-discr ete nonlinear integrable system to the modeling of transport phenomena in long macromolecules or other quasi-one-dimensional physical objects\, we s uggested rather sophisticated multistage transformation to the semi-discre te nonlinear integrable system\, characterized by the canonical Poisson st ructure and physically motivated field functions as well as by the standar d canonical Hamiltonian formulation [3\, 4\, 5\, 6]. As a result\, we obta ined two distinct but physically equivalent realizations of canonized semi -discrete four-component nonlinear integrable system\, each one being mani fested by a pronounced symmetry breaking between the so-called strong two- component and weak two-component subsystems. The rate of symmetry breaking is governed by the nonnegatively defined background parameter µν\, so t hat for µν = 0 the symmetry between subsystems becomes totally restored. We believe\, the value of background parameter µν could be regulated by external conditions imposed on a lattice. For undercritical values µν 1 of background parameter µν each particular canonized system demonstrat es bright excitation regime in strong subsystem and dark excitation regime in weak subsystem. The crossover between the bright–bright and bright –dark regimes of excitation dynamics established for the case of attract ive nonlinearity occurs in the very critical point µν = 1.\n\nReferences \n[1] O.O. Vakhnenko. Integrable nonlinear Schr¨odinger system on a trian gular-lattice ribbon\, J. Phys. Soc. Japan 84(1)\, 014003 (12 pages) (2015 ).\n[2] O.O. Vakhnenko. Nonlinear integrable model of Frenkel-like excitat ions on a ribbon of triangular lattice\, J. Math. Phys. 56(3)\, 033505 (21 pages) (2015).\n[3] O.O. Vakhnenko. Symmetry-broken canonizations of the semi-discrete integrable nonlinear Schr¨odinger system with background-co ntrolled intersite coupling\, J. Math. Phys. 57(11)\, 113504 (16 pages) (2 016).\n[4] O.O. Vakhnenko. Semi-discrete integrable nonlinear Schr¨odinge r system with background-controlled inter-site resonant coupling\, J. Nonl in. Math. Phys. 24(2)\, 250–302 (2017).\n[5] O.O. Vakhnenko. Distinctive features of the integrable nonlinear Schr¨odinger system on a ribbon of triangular lattice\, Ukr. J. Phys. 62(3)\, 271–282 (2017).\n[6] O.O. Vak hnenko\, V.O. Vakhnenko\, and A.P. Verchenko. Physical insight into the se mi-discrete nonlinear integrable systems with the true and false multicomp onentness\, Chaos Solitons Fractals 200(2)\, 117043 (24 pages) (2025).\n\n https://indico.bitp.kiev.ua/event/18/contributions/504/ LOCATION:Bogolyubov Institute for Theoretical Physics Conference Hall URL:https://indico.bitp.kiev.ua/event/18/contributions/504/ END:VEVENT END:VCALENDAR