Integrable systems and zero-curvature equations. (Spanish. English summary) Zbl 0696.58020
Summary: We consider the construction of integrable systems analogous to the equations of the Korteweg-de Vries type and others. We analyze the zero- curvature equations in the Lie bialgebra associated to a Yang-Baxter equation. It is shown that those equations may be solved in terms of a Riemannian-Hilbert problem of the appropriate Lie group.
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
