Abstract
The AKNS-KN coupling system is obtained on the base of zero curvature equation by enlarging the spectral equation. Under the Bargmann symmetry constraint, the AKNS-KN coupling system is decomposed into two integrable Hamiltonian systems with the corresponding variablesx,tnand the finite dimensional Hamiltonian systems are Liouville integrable.
Highlights
Since the integrable coupling definition is proposed, we have got many integrable coupling systems
−Gi − Niλ Ei + Fiλ −Ci − Diλ Ai + Biλ where T means the transpose of matrix and ψ = (ψ1, ψ2, ψ3, ψ4)T
In order to prove that nonlinearized system is completely integrable in the Liouville sense, we choose the following Poisson bracket:
Summary
Since the integrable coupling definition is proposed, we have got many integrable coupling systems. The exact solutions, Darboux transformation, and Hamiltonian structure of these coupling systems have been obtained [1,2,3]. In 2008, the AKNS-KN coupling system is obtained by the loop algebra whose Hamiltonian system is received with the variational identity [4]. We design a proper spectrum equation and obtain the AKNS-KN coupling system under the zero curvature equation, but the recursive operator is different from the operator of [4]. We especially list the special cases, such as AKNS integrable coupling system and KN integrable coupling system
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