Integrable nonlinear triplet lattice system with the combined inter-mode couplings

Abstract

In this article we introduce the nonlinear model of three dynamical subsystems coupled both in their kinetic and potential parts. Due to the quasi-one-dimensional spatial structure of its underlying lattice, the model grasps several degrees of freedom capable to imitate the dynamical behavior of long macromolecules both natural and synthesized origins. The model admits a clear Hamiltonian formulation with the standard form of fundamental Poisson brackets and it demonstrates the complex-conjugate symmetry between two subsystems of a Toda type. The integrability of system equations is supported by their zero-curvature representation based upon the auxiliary linear problem with the relevant spectral operator of third order. In view of these facts, we have developed an appropriate twofold Darboux–Backlund dressing technique capable to generate the nontrivial crop solution embracing all three coupled subsystems. The explicit crop solution to the nonlinear model is found to be of a pronounced pulson character.