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Enlarging spectral problems to construct integrable couplings of soliton equations. (English) Zbl 1042.37057
Summary: A way to construct integrable couplings of soliton equations is presented through enlarging spectral problems associated with soliton equations, and it is used to construct a class of integrable couplings of the AKNS soliton equations.

37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q51 Soliton equations
AKNS equations
Full Text: DOI
[1] Ma, W.X., Methods appl. anal., 7, 21, (2000)
[2] Ma, W.X., J. math. phys., 43, 1408, (2002)
[3] Olver, P.J., Applications of Lie groups to differential equations, Graduate texts in mathematics, 107, (1986), Springer-Verlag New York · Zbl 0656.58039
[4] Ablowitz, M.J.; Clarkson, P.A., Solitons, nonlinear evolution equations and inverse scattering, London mathematical society lecture note series, 149, (1991), Cambridge Univ. Press Cambridge · Zbl 0762.35001
[5] Ma, W.X., J. phys. A: math. gen., 26, 2573, (1993)
[6] Ma, W.X., J. math. phys., 33, 2464, (1992)
[7] Fokas, A.S., Stud. appl. math., 77, 253, (1987)
[8] Ma, W.X.; Strampp, W., Phys. lett. A, 185, 277, (1994)
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