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An Eight Component Integrable Hamiltonian Hierarchy from a Reduced Seventh-Order Matrix Spectral Problem

DOI: 10.4236/jamp.2024.126128, PP. 2102-2111

Keywords: Matrix Spectral Problem, Zero Curvature Equation, Lax Pair, Integrable Hierarchy, NLS Equations, mKdV Equations, Hamiltonian Structure, Lie Bracke

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Abstract:

We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schr?dinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.

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