Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies

Shou-Ting Chen and Wen-Xiu Ma ()
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Shou-Ting Chen: School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221008, China
Wen-Xiu Ma: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Mathematics, 2023, vol. 11, issue 8, 1-9

Abstract: Starting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation. To guarantee the Liouville integrability of the obtained hierarchies, the trace identity is used to establish their Hamiltonian structures. Illuminating examples of coupled nonlinear Schrödinger equations and coupled modified Korteweg–de Vries equations are worked out.

Keywords: Lax pair; zero-curvature equation; integrable hierarchy NLS equations; mKdV equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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