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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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A Few Notes on Lax Integrability, Integrable Couplings and Computing Formula of the Constant γ

Journal of Applied Nonlinear Dynamics 1(4) (2012) 401--406 | DOI:10.5890/JAND.2012.06.003

F.K. Guo$^{1}$, B.L. Feng$^{2}$, T.T. Guo$^{3}$

$^{1}$ Information School, Shandong University of Science and Technology, Qingdao 266510, China

$^{2}$ School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China

$^{3}$ Business College of Shanxi University, Taiyuan 030031, China

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We point out in the paper that the current available definition on Lax integrability is necessary to be modified; the existed method for generating integrable couplings by the approach “original equations + symmetric equations” is wrong. Besides, a simple and efficient formula for calculating the constant γ appearing in the trace identity and the quadratic-form identity is proposed, which is universal for finding Hamiltonian structures of integrable dynamics.


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  3. [3]  Guo, F.K. and Zhang, Y.F. (2002), A type of expanding integrable model of the AKNS hierarchy, Acta Physica Sinica, 51, 951-954.
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