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Nonlinear bi-integrable couplings with Hamiltonian structures

Author

Listed:
  • Ma, Wen-Xiu
  • Meng, Jinghan
  • Zhang, Mengshu

Abstract

Bi-integrable couplings of soliton equations are presented through introducing non-semisimple matrix Lie algebras on which there exist non-degenerate, symmetric and ad-invariant bilinear forms. The corresponding variational identity yields Hamiltonian structures of the resulting bi-integrable couplings. An application to the AKNS spectral problem gives bi-integrable couplings with Hamiltonian structures for the AKNS equations.

Suggested Citation

  • Ma, Wen-Xiu & Meng, Jinghan & Zhang, Mengshu, 2016. "Nonlinear bi-integrable couplings with Hamiltonian structures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 127(C), pages 166-177.
    • Handle: RePEc:eee:matcom:v:127:y:2016:i:c:p:166-177
    DOI: 10.1016/j.matcom.2013.11.007
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    References listed on IDEAS

    as
    1. Zhang, Yufeng & Tam, Honwah, 2009. "Coupling commutator pairs and integrable systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1109-1120.
    2. 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.
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