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A direct method for constructing three-gap solutions of nonlinear equations. (English. Russian original) Zbl 1042.37532

Sib. Math. J. 38, No. 5, 988-992 (1997); translation from Sib. Mat. Zh. 38, No. 5, 1140-1145 (1997).

MSC:

37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
14H52 Elliptic curves
35Q53 KdV equations (Korteweg-de Vries equations)
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[1] B. A. Bubrovin, ”Theta functions and nonlinear equations,” Uspekhi Mat. Nauk36, No.2, 11–80 (1981).
[2] B. A. Dubrovin and S. M. Natanzon, ”Real two-gap solutions of the sine-Gordon equation,” Funktsional. Anal. i Prolozhen.16, No.1, 27–43 (1982). · Zbl 0554.35100
[3] M. V. Babich, ”Effectivization of formulas for finite-gap integration of the sine-Gordon equation for a curve of genus 3,” Funktsional. Anal. i Prilozhen.19, No.3, 53–55 (1985).
[4] I. A. Taîmanov, ”Effectivization of theta-function formulas for two-dimensional Schrödinger potential operators that are finite-gap at a certain energy level,” Dokl. Akad. Nauk SSSR285, No. 5, 1067–1070 (1985). · Zbl 0611.35013
[5] I. A. Taîmanov, ”Varieties of branched coverings and nonlinear equations,” MaT. Sb.181, No.7, 934–950 (1990). · Zbl 0711.35044
[6] R. K. Romanovskiî and S. G. Sadovnichuk, ”A direct method for constructing two-gap solutions of nonlinear equations”, submitted to VINITI on December 6, 1995, No. 3234.
[7] D. Mumford, Tata Lectures on Theta [Russian translation], Mir, Moscow (1988).
[8] R. Hirota, ”Direct methods in soliton theory,” in: Solitons [Russian translation], Mir, Moscow, 1983, pp. 175–192.
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