A combined Liouville integrable hierarchy associated with a fourth-order matrix spectral problem
Wen‐Xiu Ma
Abstract
Abstract This paper aims to propose a fourth-order matrix spectral problem involving four potentials and generate an associated Liouville integrable hierarchy via the zero curvature formulation. A bi-Hamiltonian formulation is furnished by applying the trace identity and a recursion operator is explicitly worked out, which exhibits the Liouville integrability of each model in the resulting hierarchy. Two specific examples, consisting of novel generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations, are given.
Topics & Concepts
Integrable systemHierarchyMathematicsTRACE (psycholinguistics)Nonlinear systemMathematical physicsHamiltonian (control theory)Applied mathematicsCurvatureMatrix (chemical analysis)Operator (biology)Pure mathematicsPhysicsQuantum mechanicsMathematical optimizationComposite materialLinguisticsChemistryMaterials scienceGeometryEconomicsBiochemistryMarket economyPhilosophyTranscription factorGeneRepressorNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum Mechanics and Non-Hermitian Physics