Four-component integrable hierarchies of Hamiltonian equations with ($$m+n+2$$)th-order Lax pairs
Wen‐Xiu Ma
Abstract
A class of higher-order matrix spectral problems is formulated and the associated integrable hierarchies are generated via the zero-curvature formulation. The trace identity is used to furnish Hamiltonian structures and thus explore the Liouville integrability of the obtained hierarchies. Illuminating examples are given in terms of coupled nonlinear Schrödinger equations and coupled modified Korteweg–de Vries equations with four components.
Topics & Concepts
Integrable systemLax pairMathematicsHamiltonian (control theory)Mathematical physicsCurvatureNonlinear systemIdentity matrixDispersionless equationTrace classEigenvalues and eigenvectorsTRACE (psycholinguistics)Pure mathematicsClass (philosophy)Mathematical analysisPhysicsKadomtsev–Petviashvili equationQuantum mechanicsDifferential equationGeometryHilbert spacePhilosophyComputer scienceArtificial intelligenceBurgers' equationLinguisticsMathematical optimizationNonlinear Waves and SolitonsNonlinear Photonic SystemsNumerical methods for differential equations