New Integrable Nonlinear Lattice Systems with Two Adjustable Coupling Parameters

• Main Author: Vakhnenko Oleksiy O.
• Format: Article
• Language: English
• Published: De Gruyter 2013-12-01
• Series: Nonlinear Engineering
• Subjects: semidiscrete integrable nonlinear model; zero-curvature equation; local conservation laws; symmetric parametrization
• Online Access: https://doi.org/10.1515/nleng-2013-0013

The double reduction when having been applied to the fourth-order spectral operator on a discrete spatial support is shown to inspire early unknown multicomponent semidiscrete integrable nonlinear systems associated with the nonsinglular spectral operator of third order and characterized by an additional coupling parameter. Two forms of zero-curvature representation yielding the proposed integrable systems are given. Relying upon the lowest local conservation laws the selfconsistent system with the symmetric parametrization of field amplitudes is selected. The variativity of its coupling parameters is expected to ensure a number of qualitatively distinct regimes of system nonlinear dynamics.