Nonlinear integrable systems containing the canonical subsystems of distinct physical origins

Abstract

Four new semi-discrete nonlinear integrable systems relevant for physical applications are suggested. Each system contains two coupled subsystems of distinct physical origin. These integrable hybridizations are (1) the Toda-like subsystem coupled with the induced-trapping subsystem of PT-symmetric excitations, (2) the subsystem of Frenkel-like excitons coupled with the subsystem of nontrivial vibrations, (3) two coupled self-trapping subsystems, (4) the Toda-like subsystem coupled with the self-trapping subsystem akin to the charged particle with electromagnetic field. Each hybrid system admits the clear Hamiltonian representation characterized by two pairs of canonical field variables with the standard Poisson structure. The main general local conserved densities, adaptable to any integrable system under consideration, are found explicitly.