An Integrated Integrable Hierarchy Arising from a Broadened Ablowitz–Kaup–Newell–Segur Scenario
Wen‐Xiu Ma
Abstract
This study introduces a 4×4 matrix eigenvalue problem and develops an integrable hierarchy with a bi-Hamiltonian structure. Integrability is ensured by the zero-curvature condition, while the Hamiltonian structure is supported by the trace identity. Explicit derivations yield second-order and third-order integrable equations, illustrating the integrable hierarchy.
Topics & Concepts
Integrable systemHierarchyMathematicsCurvatureEigenvalues and eigenvectorsHamiltonian (control theory)Pure mathematicsTRACE (psycholinguistics)Hamiltonian systemMathematical physicsAlgebra over a fieldMathematical analysisPhysicsGeometryQuantum mechanicsMathematical optimizationEconomicsMarket economyPhilosophyLinguisticsNonlinear Waves and SolitonsNumerical methods for differential equationsNonlinear Photonic Systems