A combined integrable hierarchy with four potentials and its recursion operator and bi-Hamiltonian structure

Based on a specific matrix Lie algebra, we propose a spectral matrix with four potentials and generate its associated Liouville integrable Hamiltonian hierarchy. The zero curvature formulation and the trace identity are the basic tools. The Liouville integrability of the resulting hierarchy is shown...

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Bibliographic Details
Published inIndian journal of physics Vol. 99; no. 3; pp. 1063 - 1069
Main Author Ma, Wen-Xiu
Format Journal Article
LanguageEnglish
Published West Bengal Springer Nature B.V 01.03.2025
Subjects
Integral equations
Korteweg-Devries equation
Lie groups
Matrix algebra
Operators (mathematics)
Schrodinger equation
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Summary:Based on a specific matrix Lie algebra, we propose a spectral matrix with four potentials and generate its associated Liouville integrable Hamiltonian hierarchy. The zero curvature formulation and the trace identity are the basic tools. The Liouville integrability of the resulting hierarchy is shown by determining its recursion operator and bi-Hamiltonian structure. Two illustrative examples of generalized combined nonlinear Schrödinger equations and modified Korteweg-de Vries equations are explicitly presented. The success lies in introducing a specific 4×4 spectral matrix which keads to an integrable hierarchy.
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ISSN:0973-1458
0974-9845
DOI:10.1007/s12648-024-03364-4