A new integrable symplectic map for 4-field Blaszak-Marciniak lattice equations. (English) Zbl 1457.37088
Summary: Based on a new discrete \(4\times 4\) matrix spectral problem, a hierarchy of integrable 4-field Blaszak-Marciniak lattice equations with four potentials is constructed. Moreover, a new integrable symplectic map and its evolutive system of conserved integrals are obtained by the binary nonlinearization of spatial parts and the time parts of Lax pairs and their adjoint Lax pairs of the hierarchy.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
4-field Blaszak-Marciniak lattice equation; discrete zero-curvature representation; binary nonlinearization; integrable symplectic mapReferences:
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