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:
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