Low-amplitude instability as a premise for the spontaneous symmetry breaking in the new integrable semidiscrete nonlinear system |
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| Affiliation: | 1. Quantum Electronics Department, Bogolyubov Institute for Theoretical Physics, 14-B Metrologichna Street, Kyïv 03680, Ukraine;2. Department of Dynamics of Deformable Solids, Subbotin Institute of Geophysics, 63-B Bohdan Khmel’nyts’kyy Street, Kyïv 01054, Ukraine;1. Department of Food Science, Design and Consumer Behavior, University of Copenhagen, Rolighedsvej 26, DK-1958 Frederiksberg C, Denmark;2. Irish Seaweed Kitchen, Streedagh House, Streedagh, Grange, Co. Sligo, Ireland, UK;3. Instituto Universitario de Investigación Marina (INMAR), Campus de Excelencia Internacional/Global del Mar (CEI·MAR), Universidad de Cádiz, Av. República Saharaui s/n, 11510 Puerto Real, Cádiz, Spain;1. Department of Organic Chemistry, Poznan University of Medical Sciences, 60-780 Poznań, Poland;2. Department of Materials Chemistry, Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland;1. School of Chemistry, Chemical Engineering and Life Sciences, Wuhan University of Technology, Wuhan 430070, China;2. Department of Anatomy, College of Medicine, Huazhong University of Science and Technology, Wuhan 430074, China |
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| Abstract: | The new integrable semidiscrete multicomponent nonlinear system characterized by two coupling parameters is presented. Relying upon the lowest local conservation laws the concise form of the system is given and its selfconsistent symmetric parametrization in terms of four independent field variables is found. The comprehensive analysis of quartic dispersion equation for the system low-amplitude excitations is made. The criteria distinguishing the domains of stability and instability of low-amplitude excitations are formulated and a collection of qualitatively distinct realizations of a dispersion law are graphically presented. The loop-like structure of a low-amplitude dispersion law of reduced system emerging within certain windows of adjustable coupling parameter turns out to resemble the loop-like structure of a dispersion law typical of beam-plasma oscillations. Basing on the peculiarities of low-amplitude dispersion law as the function of adjustable coupling parameter it is possible to predict the windows of spontaneous symmetry breaking even without an explicit knowledge of the system Lagrangian function. Having been rewritten in terms of properly chosen modified field variables the reduced four wave integrable system can be qualified as consisting of two coupled nonlinear lattice subsystems, namely the self-dual ladder network and the vibrational ones. |
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