Sadovnichuk, S. G. 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) PDFBibTeX XMLCite \textit{S. G. Sadovnichuk}, Sib. Math. J. 38, No. 5, 1140--1145 (1997; Zbl 1042.37532); translation from Sib. Mat. Zh. 38, No. 5, 1140--1145 (1997) Full Text: DOI References: [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. 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.