Prototype and reduced nonlinear integrable lattice systems with the modulated pulson behavior

• Published in: Wave motion 2021-07, Vol.104, p.102745, Article 102745
• Main Author: Vakhnenko, Oleksiy O.
• Format: Article
• Language: English
• Subjects: Conservation laws; Couplings; Darboux–Bäcklund transformation; Lagrangian and Hamiltonian representations; Lattice theory; Modulated pulson; Nonlinear systems; Prototypes; Semi-discrete nonlinear integrable system; Subsystems; Ternary systems
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2021.102745

A multi-component semi-discrete nonlinear integrable system associated with the relevant third-order auxiliary linear problem is claimed to be the prototype system for several reduced integrable systems formulated in terms of true dynamical field variables. The main conservation laws related to the prototype system are found in the framework of generalized recurrent approach. The two-fold Darboux–Bäcklund dressing technique as applied to the integration of prototype system is developed in details. The novel reduced complex-valued nonlinear integrable system embracing three coupled dynamical subsystems on a quasi-one-dimensional lattice is proposed and its concise Lagrangian and Hamiltonian representations are written down. The essentially nontrivial couplings between the two complex-valued Toda-like subsystems are shown to be mediated by the intermediate subsystem both in their kinetic and potential parts. The explicit multi-component solution of a modulated pulson type related to the reduced integrable nonlinear ternary system is presented and analyzed. •The novel reduced integrable multi-component dynamical nonlinear lattice system is suggested.•The main conservation laws of the prototype system are recovered by the generalized recurrent technique.•The two-fold Darboux–Bäcklund dressing approach to the system’s integration is developed in details.•The complex-valued Lagrangian and Hamiltonian representations of the reduced system are obtained.•The modulated pulson type of multi-component solution is introduced and explicitly found.