integrable system Jacobian derivation 2 Lie algebra 2 Primary 17B66 2 Secondary 17B80 2 centralizer 2 differential equation 2 iнтеґровна система 2 nonlinear dynamics 2 нелiнiйна динамiка 2 02.30.Ik 1 02.30.Oz 1 05.45.Yv 1 11.30.-j 1 45.05. x 1 45.20.Jj 1 Hamiltonian dynamics 1 PACS numbers: 11.10.Lm 1 canonical field variables 1 conservation laws 1 nonlinear lattice 1 parametric drive 1 quasi-one-dimensional lattice 1 soliton 1 stable displacements 1 symmetry breaking 1 two-leg ladder lattice 1 unstable displacements 1 Гамiльтонова динамiка 1 двонiжкова драбинчата ґратка 1