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A simple method to construct integrable coupling system for the MKdV equation hierarchy. (English) Zbl 1179.37089

The author extends W. X. Ma’s and F. K. Guo’s method [Int. J. Theor. Phys. 36, No. 3, 697–704 (1997; Zbl 0946.37032)] to construct the integrable couplings of the soliton equation hierarchy with the Kronecker product and two-nilpotent matrix. A direct application to the MKdV spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is shown that the study of integrable couplings using the Kronecker product is an efficient and straightforward method.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Citations:

Zbl 0946.37032
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References:

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