Wisse, M. A. Quasiperiodic solutions for matrix nonlinear Schrödinger equations. (English) Zbl 0762.35112 J. Math. Phys. 33, No. 11, 3694-3699 (1992). Summary: The Adler-Kostant-Symes theorem yields isospectral Hamiltonian flows on the dual \(\tilde{\mathfrak g}^{+*}\) of a Lie subalgebra \(\tilde{\mathfrak g}^ +\) of a loop algebra \(\tilde{\mathfrak g}\). A general approach relating the method of integration of I. M. Krichever, and S. P. Novikov [Russ. Math. Surv. 35, No. 6, 53-79 (1980; Zbl 0548.35100)], and B. A. Dubrovin [ibid. 36, No. 2, 11-92 (1981; Zbl 0549.58038)]to such flows is used to obtain finite-gap solutions of matrix nonlinear Schrödinger equations in terms of quotients of \(\theta\) functions. Cited in 4 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37C10 Dynamics induced by flows and semiflows 14H42 Theta functions and curves; Schottky problem Keywords:Krichever method; isospectral Hamiltonian flows; finite-gap solutions Citations:Zbl 0548.35100; Zbl 0549.58038 PDFBibTeX XMLCite \textit{M. A. Wisse}, J. Math. Phys. 33, No. 11, 3694--3699 (1992; Zbl 0762.35112) Full Text: DOI arXiv References: [1] DOI: 10.1007/BF02098447 · Zbl 0717.58051 [2] DOI: 10.1070/RM1980v035n06ABEH001974 · Zbl 0548.35100 [3] DOI: 10.1070/RM1981v036n02ABEH002596 · Zbl 0549.58038 [4] DOI: 10.1007/BF01223376 · Zbl 0659.58022 [5] DOI: 10.1007/BF01214664 · Zbl 0563.35062 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.