Geodesic
Four-component integrable hierarchies of Hamiltonian equations with ($m+n+2$)th-order Lax pairs
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 315-325

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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 Schrödinger equations and coupled modified Korteweg–de Vries equations with four components.
Mots-clés : Lax pair, NLS equations, mKdV equations.
Keywords: zero-curvature equation, integrable hierarchy, Hamiltonian structure 
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     author = {Wen-Xiu Ma},
     title = {Four-component integrable hierarchies of {Hamiltonian} equations with ($m+n+2$)th-order {Lax} pairs},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {315--325},
     publisher = {mathdoc},
     volume = {216},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a8/}
}
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Wen-Xiu Ma. Four-component integrable hierarchies of Hamiltonian equations with ($m+n+2$)th-order Lax pairs. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 315-325. http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a8/