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Symmetric reductions of the Riemann $$\theta$$-function and some of their applications to the Schrödinger and Boussinesq equations. (English) Zbl 0807.35137
Birman, M. Sh. (ed.), Wave propagation. Scattering theory. Transl. from the Russian by Peter Zhevandrov. Transl. ed. by Simeon Ivanov. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 157, 227-237 (1993).
Summary: Main ideas of reduction of finite-gap almost periodic solutions to elliptic functions for curves possessing a nontrivial conformal automorphism group by means of the Appell theorem and its matrix analog are given in this paper. Particular applications to the Boussinesq and nonlinear Schrödinger equation are considered. For the first time a real multiparametric nonhyperelliptic solution of the Boussinesq equation expressed via elliptic functions is obtained.
For the entire collection see [Zbl 0788.00073].

##### MSC:
 35Q55 NLS equations (nonlinear Schrödinger equations) 35B15 Almost and pseudo-almost periodic solutions to PDEs 14H42 Theta functions and curves; Schottky problem