Dubrovin, B. A. [Krichever, I. M.] Theta-functions and non-linear equations. (Russian) Zbl 0478.58038 Usp. Mat. Nauk 36, No. 2(218), 11-80 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 107 Documents MSC: 58J99 Partial differential equations on manifolds; differential operators 35Q99 Partial differential equations of mathematical physics and other areas of application 35C99 Representations of solutions to partial differential equations 35B99 Qualitative properties of solutions to partial differential equations 14H52 Elliptic curves 14H40 Jacobians, Prym varieties 53C22 Geodesics in global differential geometry 30F99 Riemann surfaces Keywords:theta-functions; Riemann motions; nonlinear differential equations; Schrödinger equation; theta-functions of Riemann surfaces; two-zone potentials; Kowalevsky problem; geodesics on an ellipsoid; non-abelian Toda lattice PDFBibTeX XMLCite \textit{B. A. Dubrovin}, Usp. Mat. Nauk 36, No. 2(218), 11--80 (1981; Zbl 0478.58038) Digital Library of Mathematical Functions: §21.1 Special Notation ‣ Notation ‣ Chapter 21 Multidimensional Theta Functions §21.6(ii) Addition Formulas ‣ §21.6 Products ‣ Properties ‣ Chapter 21 Multidimensional Theta Functions §21.7(i) Connection of Riemann Theta Functions to Riemann Surfaces ‣ §21.7 Riemann Surfaces ‣ Applications ‣ Chapter 21 Multidimensional Theta Functions Figure 21.9.2 ‣ §21.9 Integrable Equations ‣ Applications ‣ Chapter 21 Multidimensional Theta Functions Figure 21.9.2 ‣ §21.9 Integrable Equations ‣ Applications ‣ Chapter 21 Multidimensional Theta Functions §21.9 Integrable Equations ‣ Applications ‣ Chapter 21 Multidimensional Theta Functions §21.9 Integrable Equations ‣ Applications ‣ Chapter 21 Multidimensional Theta Functions Chapter 21 Multidimensional Theta Functions Sidebar 21.SB2: A two-phase solution of the Kadomtsev–Petviashvili equation (21.9.3) ‣ Chapter 21 Multidimensional Theta Functions Notations T ‣ Notations