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A combined Liouville integrable hierarchy associated with a fourth-order matrix spectral problem

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This paper aims to propose a fourth-order matrix spectral problem involving four potentials and generate an associated Liouville integrable hierarchy via the zero curvature formulation.A bi-Hamiltonian formulation is furnished by applying the trace identity and a recursion operator is explicitly worked out,which exhibits the Liouville integrability of each model in the resulting hierarchy.Two specific examples,consisting of novel generalized combined nonlinear Schrödinger equations and modified Korteweg-de Vries equations,are given.

integrable hierarchyHamiltonian structurezero curvature equationLax pairmatrix spectral problem

Wen-Xiu Ma

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Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China

Department of Mathematics,King Abdulaziz University,Jeddah 21589,Saudi Arabia

Department of Mathematics and Statistics,University of South Florida Tampa,FL 33620-5700,United States of America

Material Science Innovation and Modelling,Department of Mathematical Sciences,North-West University,Mafikeng Campus,Mmabatho 2735,South Africa

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NSFCNSFCNSFCMinistry of Science and Technology of ChinaMinistry of Science and Technology of ChinaNatural Science Foundation for Colleges and Universities in Jiangsu Province

122714881197514511972291G2021016032LG2023016011L17 KJB 110020

2024

10.1088/1572-9494/ad3dd9

理论物理通讯(英文版)
中国科学院理论物理研究所 中国物理学会

理论物理通讯(英文版)

CSTPCD
影响因子：0.333
ISSN：0253-6102
年,卷(期)：2024.76(7)