A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem
Wen‐Xiu Ma
Abstract
The aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formulation. A hereditary recursion operator is explicitly computed, and the corresponding bi-Hamiltonian formulation is established by the so-called trace identity, showing the Liouville integrability of the obtained hierarchy. Two illustrative examples are novel generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations with four components and two adjustable parameters.
Topics & Concepts
Integrable systemHierarchyMathematicsHamiltonian (control theory)Matrix (chemical analysis)Order (exchange)Camassa–Holm equationPure mathematicsMathematical physicsApplied mathematicsAlgebra over a fieldMathematical optimizationMaterials sciencePolitical scienceComposite materialLawFinanceEconomicsMatrix Theory and AlgorithmsSpectral Theory in Mathematical PhysicsDifferential Equations and Boundary Problems