New Matrix Lax Representation for a Blaszak–Marciniak Four-Field Lattice Hierarchy and Its Infinitely Many Conservation Laws

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lattice dynamics; integrable lattice equations (37K60)

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Explicit solutions for a semidiscrete Boussinesq system ⋮ New lattice equation hierarchies and Darboux transformation ⋮ A hierarchy of lattice soliton equations associated with a new discrete eigenvalue problem and Darboux transformations ⋮ Matrix spectral problems and integrability aspects of the Błaszak-Marciniak lattice equations ⋮ A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy ⋮ Two hierarchies of lattice soliton equations associated with a new discrete eigenvalue problem and Darboux transformation ⋮ A hierarchy of discrete Hamiltonian equations and its binary nonlinearization by symmetry constraint ⋮ New hierarchies of integrable positive and negative lattice models and Darboux transformation ⋮ The integrable coupling system of a \(3 \times 3\) discrete matrix spectral problem ⋮ Hamiltonian structure and infinite number of conservation laws for the coupled discrete KdV equations ⋮ A new integrable symplectic map for 4-field Blaszak-Marciniak lattice equations ⋮ A HIERARCHY OF DISCRETE INTEGRABLE SYSTEM AND ITS COUPLED ENLARGED INTEGRABLE SYSTEM ⋮ A NEW HIERARCHY OF DISCRETE INTEGRABLE MODEL AND ITS DARBOUX TRANSFORMATION ⋮ Positive and negative integrable hierarchies, associated conservation laws and Darboux transformation ⋮ INTEGRABLE EXPANDING MODELS FOR DISCRETE SYSTEMS APPLICATION: COUPLED TODA AND RELATIVISTIC TODA LATTICE ⋮ A super-discrete variational identity and its application for constructing super-discrete Hamiltonian systems ⋮ Infinitely many conservation laws for two integrable lattice hierarchies associated with a new discrete Schrödinger spectral problem

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