FOUR-COMPONENT INTEGRABLE HIERARCHIES OF HAMILTONIAN EQUATIONS WITH (m + n+2)TH-ORDER LAX PAIRS

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 Schrodinger equations and coupled modified Korteweg-de Vries equations with four components.

Automated summary

This paper formulates a class of higher-order matrix spectral problems and generates associated integrable hierarchies using the zero-curvature formulation. Hamiltonian structures are obtained using the trace identity to explore the Liouville integrability of the obtained hierarchies. Illuminating examples are provided using coupled nonlinear Schrodinger equations and coupled modified Korteweg-de Vries equations with four components.