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An extended AKNS eigenvalue problem and its affiliated integrable Hamiltonian hierarchies

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  • Ma, Wen-Xiu

Abstract

This paper aims to study an extended 4 × 4 AKNS eigenvalue problem and construct its affiliated integrable hierarchies of bi-Hamiltonian models over the real field. The Lax pair framework serves as the fundamental tool, ensuring integrability through bi-Hamiltonian structures with hereditary recursion operators. We compute illustrative examples of lower-order equations to demonstrate the affiliated integrable hierarchies.

Suggested Citation

  • Ma, Wen-Xiu, 2024. "An extended AKNS eigenvalue problem and its affiliated integrable Hamiltonian hierarchies," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924011329
    DOI: 10.1016/j.chaos.2024.115580
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    References listed on IDEAS

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    1. Xia, Tiecheng & Yu, Fajun & Zhang, Yi, 2004. "The multi-component coupled Burgers hierarchy of soliton equations and its multi-component integrable couplings system with two arbitrary functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 238-246.
    2. Yang, Sheng-Xiong & Wang, Yu-Feng & Zhang, Xi, 2023. "Conservation laws, Darboux transformation and localized waves for the N-coupled nonautonomous Gross–Pitaevskii equations in the Bose–Einstein condensates," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Ma, Wen-Xiu, 2024. "Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    4. Zhang, Houchao & Shi, Dongyang & Li, Qingfu, 2020. "Nonconforming finite element method for a generalized nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 377(C).
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