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A 3 sx 3 matrix spectral problem for AKNS hierarchy and its binary nonlinearization

Author

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  • Ma, W.X.
  • Fuchssteiner, B.
  • Oevel, W.

Abstract

A 3 × 3 matrix spectral problem for AKNS soliton hierarchy is introduced and the corresponding Bargmann symmetry constraint involving Lax pairs and adjoint Lax pairs is discussed. An explicit new Poisson algebra is proposed and thus the Liouville integrability is established for the nonlinearized spatial system ind a hierarchy of nonlinearized temporal systems under the control of the nonlinearized spatial system. The obtained nonlinearized Lax systems, in which the nonlinearized spatial system is intimately related to stationary AKNS flows, lead to a sort of new involutive solutions to each AKNS soliton equation. Therefore, the binary nonlinearization theory is successfully extended to a case of 3 × 3 matrix spectral problem for AKNS hierarchy.

Suggested Citation

  • Ma, W.X. & Fuchssteiner, B. & Oevel, W., 1996. "A 3 sx 3 matrix spectral problem for AKNS hierarchy and its binary nonlinearization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 233(1), pages 331-354.
    • Handle: RePEc:eee:phsmap:v:233:y:1996:i:1:p:331-354
    DOI: 10.1016/S0378-4371(96)00225-7
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    Cited by:

    1. Cao, Jianli & Shi, Wei, 2013. "A new integrable generalized Neumann system related to soliton hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 13-17.
    2. Zeng, Yunbo & Ma, Wen-Xiu, 1999. "The construction of canonical separated variables for binary constrained AKNS flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(3), pages 505-515.

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