The integrable coupling system of a 3 × 3 discrete matrix spectral problem |
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Authors: | Qiu-Lan Zhao Xin-Zeng Wang |
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Institution: | a College of Science, Shandong University of Science and Technology, Qingdao 266510, PR China b College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, PR China |
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Abstract: | Integrable coupling with six potentials is first proposed by coupling a given 3 × 3 discrete matrix spectral problem. It is shown that coupled system of integrable equations can possess zero curvature representations and recursion operators, which yield infinitely many commuting symmetries. Moreover, by means of the discrete variational identity on semi-direct sums of Lie algebras, the Hamiltonian form is deduced for the lattice equations in the resulting hierarchy. Finally, we prove that the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian system. |
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Keywords: | Integrable couplings Discrete variational identity Discrete zero curvature representations Liouville integrable system |
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