Semidiscrete Integrable Nonlinear Systems Generated by the New Fourth-Order Spectral Operator: Local Conservation Laws

DOI10.1142/S1402925111001672zbMath1256.35141OpenAlexW2057704801MaRDI QIDQ3095757

Oleksiy O. Vakhnenko

Publication date: 3 November 2011

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1402925111001672

zbMATH Keywords

generating functionslocal conservation lawszero-curvature equationfourth-order spectral operator

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) NLS equations (nonlinear Schrödinger equations) (35Q55) Lattice dynamics; integrable lattice equations (37K60)

Related Items (12)

Low-amplitude instability as a premise for the spontaneous symmetry breaking in the new integrable semidiscrete nonlinear system ⋮ Integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell ⋮ A hierarchy of integrable differential-difference equations and Darboux transformation ⋮ Nonlinear integrable systems containing the canonical subsystems of distinct physical origins ⋮ Prototype and reduced nonlinear integrable lattice systems with the modulated pulson behavior ⋮ Six-component semi-discrete integrable nonlinear Schrödinger system ⋮ Infinite number of conservation laws and Darboux transformations for a 6-field integrable lattice system ⋮ Semidiscrete Integrable Nonlinear Systems Generated by the New Fourth Order Spectral Operator: Systems of Obverse Type ⋮ Four-Wave Semidiscrete Nonlinear Integrable System with 𝒫𝒯-Symmetry ⋮ Semi-discrete integrable nonlinear Schrödinger system with background-controlled inter-site resonant coupling ⋮ Four-component integrable systems inspired by the Toda and the Davydov-Kyslukha models ⋮ Nonlinear integrable model of Frenkel-like excitations on a ribbon of triangular lattice

Cites Work

• Infinitely many conservation laws of two Blaszak-Marciniak three-field lattice hierarchies
• The conservation laws of some discrete soliton systems.
• The Coupled Modified Korteweg-de Vries Equations
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• An exact polyhedral model for boron nanotubes
• Nonlinear differential–difference equations and Fourier analysis
• Lectures on the Inverse Scattering Transform
• Integrable semi-discretization of the coupled nonlinear Schrödinger equations
• Three-component nonlinear dynamical system generated by the new third-order discrete spectral problem
• Integrable discretizations of derivative nonlinear Schr dinger equations
• Multicomponent nonlinear dynamical systems inspired by the Toda lattice
• Integrable semi-discretization of the coupled modified KdV equations
• Inverse scattering transform for the nonlinear Schrödinger system on a zigzag-runged ladder lattice
• Integrable nonlinear ladder system with background-controlled intersite resonant coupling

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