Solving AKNS equations via Jacobi inversion problem. (English) Zbl 1010.37038
Summary: By using Lax representation, we study the separation of variables for \(x\)- and \(t_n\)-finite-dimensional integrable Hamiltonian system (FDIHS) obtained from the factorization of AKNS hierarchy. Then the separability of \(x\)- and \(t_n\)-FDIHS and the factorization of AKNS hierarchy give rise to the Jacobi inversion problem for soliton equations in AKNS hierarchy. By a standard Jacobi inversion technique, the soliton equations can be solved in terms of Riemann theta function.
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37K20 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions |
Keywords:
Lax representation; separation of variables; Hamiltonian system; factorization; soliton equationsReferences:
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