Abstract:
A method is described for constructing algebraic curves whose theta functions reduce to one-dimensional functions. This makes it possible to construct finite-gap solutions of nonlinear equations expressed in terms of the elliptic functions. Elliptic two-gap potentials of the Schrödinger operator different from the Lamé and Verdier potentials are constructed.
This publication is cited in the following 10 articles:
B. T. Saparbaeva, “Two-Dimensional Finite-Gap Schrödinger Operators with Elliptic Coefficients”, Math. Notes, 747–749
Fritz Gesztesy, Karl Unterkofler, Rudi Weikard, “An explicit characterization of Calogero–Moser systems”, Trans. Amer. Math. Soc., 358:2 (2005), 603
Gesztesy, F, “Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - An analytic approach”, Bulletin of the American Mathematical Society, 35:4 (1998), 271
Fritz Gesztesy, Rudi Weikard, “A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy”, Acta Math., 181:1 (1998), 63
A. O. Smirnov, “Elliptic in t solutions of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 107:2 (1996), 568–578
Fritz Gesztesy, Rudi Weikard, “Picard potentials and Hill's equation on a torus”, Acta Math., 176:1 (1996), 73
A. O. Smirnov, “Two-gap elliptic solutions to integrable nonlinear equations”, Math. Notes, 58:1 (1995), 735–743
F. Gesztesy, R. Weikard, “Treibich-Verdier potentials and the stationary (m)KDV hierarchy”, Math Z, 219:1 (1995), 451
A. O. Smirnov, “Elliptic solutions of the nonlinear Schrödinger equation and the modified Korteweg–de Vries equation”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 461–470
A. O. Smirnov, “Solutions of the KdV equation elliptic in t”, Theoret. and Math. Phys., 100:2 (1994), 937–947
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