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Quasiperiodic solutions for matrix nonlinear Schrödinger equations. (English) Zbl 0762.35112

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.

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
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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
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