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A kind of integrable couplings of soliton equations hierarchy with self-consistent sources associated with \(\tilde{sl}(4)\). (English) Zbl 1225.35193
Summary: A kind of integrable couplings of soliton equations hierarchy with self-consistent sources associated with \(\tilde{sl}(4)\) is presented. As an application example, the hierarchy of Yang equations with self-consistent sources is derived. Furthermore, we construct an integrable couplings of the Yang soliton hierarchy with self-consistent sources by using of the loop algebra \(\tilde{sl}(4)\).

MSC:
35Q51 Soliton equations
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35C08 Soliton solutions
22E70 Applications of Lie groups to the sciences; explicit representations
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[1] Ablowitz, M.J.; Clarkson, P.A., Soliton, nonlinear evolution equation and inverse scattering, (1991), Cambridge Univ. Press · Zbl 0762.35001
[2] Mel’nikov, V.K., Phys. lett. A, 22, 118, (1986)
[3] Mel’nikov, V.K., Commun. math. phys., 112, 639, (1987)
[4] Mel’nikov, V.K., Phys. lett. A, 113, 493, (1988)
[5] Ma, W.X., J. phys. soc. jpn., 72, 3017, (2003)
[6] Ma, W.X., Chaos solitons fractals, 26, 1453, (2005)
[7] Ma, W.X.; Fuchssteiner, B., Chaos solitons fractals, 7, 1227, (1997)
[8] Ma, W.X., Methods appl. anal., 7, 21, (2000)
[9] Ma, W.X.; Fuchssteiner, B., Phys. lett. A, 213, 49, (1996) · Zbl 0863.35106
[10] Ma, W.X., Phys. lett. A, 316, 72, (2003)
[11] Ma, W.X., J. math. phys., 46, 033507, (2005)
[12] X Ma, W.; Xu, X.X.; Zhang, Y.F., J. math. phys., 47, 053501, (2006)
[13] Ma, W.X.; Xu, X.X.; Zhang, Y.F., Phys. lett. A, 351, 125, (2006)
[14] Guo, F.G.; Zhang, Y.F., J. math. phys., 44, 5793, (2003)
[15] Yu, F.J.; Zhang, H.Q., Phys. lett. A, 353, 326, (2006)
[16] Zhang, Y.F.; Fang, E.G., Commun. theor. phys. (China), 49, 845, (2008)
[17] Yang, H.X.; Xu, X.X., Chin. phys., 14, 5, 869, (2005)
[18] Xia, T.C.; You, F.C., Chin. phys., 16, 3, 605, (2007)
[19] Xia, T.C.; Wang, H.; Zhang, Y.F., Chin. phys., 14, 2, 247, (2005)
[20] Yu, F.J.; Zhang, H.Q., Chaos solitons fractals, 33, 829, (2007)
[21] Ma, W.X.; Chen, M., J. phys. A: gen. math., 39, 10787, (2006)
[22] Ma, W.X., J. phys. A: gen. math., 40, 15055, (2007) · Zbl 1128.22014
[23] Zeng, Y.B.; Ma, W.X.; Lin, R.L., J. math. phys., 41, 5453, (2000)
[24] Tu, G.Z., J. math. phys., 33, 2, 330, (1989)
[25] Lax, P.D., Commun. pure appl. math., 28, 141, (1975)
[26] Zhang, Y.F.; Guo, F.K., Chaos solitons fractals, 34, 490, (2007)
[27] Ma, W.X., Chin. sci. bull., 36, 16, 1325, (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.