## A Liouville integrable Hamiltonian system associated with a generalized Kaup-Newell spectral problem.(English)Zbl 0977.37039

Summary: Starting from a generalized Kaup-Newell spectral problem involving an arbitrary function, we derive a hierarchy of nonlinear evolution equations, which is explicitly related to many important equations such as Kaup-Newell equation, Chen-Lee-Liu equation, Gerdjikov-Ivanov equation, Burgers equation, modified Korteweg-de Vries equation and Sharma-Tasso-Olever equation. It is also shown that the hierarchy is integrable in Liouville’s sense and possesses multi-Hamiltonian structure.

### MSC:

 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35Q53 KdV equations (Korteweg-de Vries equations)

### Keywords:

nonlinear evolution equations
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### References:

 [1] Tu, G.Z., J. math. phys., 30, 330, (1989) [2] Tu, G.Z., J. phys., A 23, 3903, (1990) [3] Gu, C.H.; Hu, H.S.; Zhou, Z.X., Darboux transformation in soliton theory and its geometric applications, (1999), Shanghai Scientific and Technical Publishers Shanghai [4] Kaup, D.J.; Newell, A.C., J. math. phys., 19, 798, (1978) [5] Zeng, Y.B., Physica, D 73, 171, (1994) [6] Chen, H.H.; Lee, Y.C.; Liu, C.S., Phys. scr., 20, 490, (1979) [7] Calogero, F.; Eckhaus, W., Inverse problems, 3, 229, (1987) [8] Kakei, S.; Sasa, N.; Satsuma, J., Phys. soc. jpn, 64, 1519, (1995) [9] Gerdjikov, V.S.; Ivanov, M.I., Bulg. J. phys., 10, 130, (1983) [10] Olever, P.J., J. math. phys., 18, 1212, (1977) [11] Yang, Z.Y., J. phys., A 27, 2837, (1994) [12] Gudkov, V.V., J. math. phys., 38, 4794, (1997)
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