A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem

Wen-Xiu Ma ()
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Wen-Xiu Ma: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Mathematics, 2024, vol. 12, issue 6, 1-12

Abstract: The aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formulation. A hereditary recursion operator is explicitly computed, and the corresponding bi-Hamiltonian formulation is established by the so-called trace identity, showing the Liouville integrability of the obtained hierarchy. Two illustrative examples are novel generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations with four components and two adjustable parameters.

Keywords: matrix spectral problem; Lax pair; integrable hierarchy; monlinear Schrödinger equations; modified Korteweg–de Vries equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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