Explicit quasi-periodic solutions of the Kaup-Newell hierarchy. (English) Zbl 1317.37088
Summary: An algebraic curve of arithmetic genus \(n\) is introduced with the aid of the Lax matrix, from which we construct the meromorphic function on the algebraic curve and investigate its properties. Further, we straighten out all the flows associated with the Kaup-Newell hierarchy under the Abel-Jacobi coordinates. Finally, we achieve the explicit quasi-periodic solutions for the whole Kaup-Newell hierarchy, including the coupled derivative nonlinear Schrödinger equations.
MSC:
| 37K30 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 14H70 | Relationships between algebraic curves and integrable systems |
| 35Q51 | Soliton equations |
| 35B15 | Almost and pseudo-almost periodic solutions to PDEs |
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