A new loop algebra system and its discrete integrable coupling system. (English) Zbl 1133.37336
Summary: A new loop algebra \(X\) is constructed, which is devoted to working out the well-known Blaszak-Marciniak lattice equations hierarchy. Then an extended algebraic system \(\widetilde X\) of \(X\) is presented, from which the integrable coupling system of the Blaszak-Marciniak lattice equations are obtained.
MSC:
37K30 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures |
17B80 | Applications of Lie algebras and superalgebras to integrable systems |
37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
Lax matrix method; discrete integrable hierarchies; Blaszak-Marciniak lattice equations hierarchyReferences:
[1] | Tu, G., J Math Phys, 30, 2, 330 (1989) · Zbl 0678.70015 |
[2] | Ma, W., Chin J Contemp Math, 13, 1, 79 (1992) |
[3] | Guo, F., Acta Math Phys, 19, 5, 507 (1999) · Zbl 0953.35136 |
[4] | Tu, G., J Phys A, 26, 3902 (1990) |
[5] | Hu, X.; Tam, H., Glasagow Math J, 43A, 43 (2001) |
[6] | Hu, X., J Math Phys, 38, 4766 (1998) |
[7] | Hu, X.; Tam, H., Phys Lett A, 276, 65 (2000) · Zbl 1119.37332 |
[8] | Tam, H.; Hu, X., J Phys Soc Jpn, 72, 265 (2003) · Zbl 1086.35113 |
[9] | Hu, X., Appl Math Lett, 13, 45 (2000) |
[10] | Hu, X., J Phys Soc Jpn, 69, 1042 (2000) |
[11] | Ma, W.; Fuchssteiner, B., J Math Phys, 40, 2400 (1999) · Zbl 0984.37097 |
[12] | Tsuchida, T.; Ujino, H.; Wadati, M., J Math Phys, 39, 4785 (1998) · Zbl 0933.35176 |
[13] | Tsuchida, T.; Ujino, H.; Wadati, M., J Phys, 32, 2239 (1999) · Zbl 0941.35112 |
[14] | Ma, W.; Fuchssteiner, B., Chaos, Solitons & Fractals, 7, 1227 (1996) · Zbl 1080.37578 |
[15] | Fuchssteiner, B., Coupling of completely integrable systems (1993), Kluwer: Kluwer Dordrecht, p. 125 · Zbl 0786.35123 |
[16] | Zhang, Y.; Zhang, H., J Math Phys, 43, 466 (2002) · Zbl 1052.37055 |
[17] | Yu, F.; Xia, T.; Zhang, H., Chaos, Solitons & Fractals, 27, 1036 (2006) · Zbl 1102.37044 |
[18] | Zhang, Y., Phys Lett A, 299, 543 (2002) · Zbl 0996.37073 |
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