Non-linear equations of Korteweg--de Vries type, finite-zone linear
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 31 (1976) no. 1, pp. 59-146
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The basic content of this survey is an exposition of a recently developed method of constructing a broad class of periodic and almost-periodic solutions of non-linear equations of mathematical physics to which (in the rapidly decreasing case) the method of the inverse scattering problem is applicable. These solutions are such that the spectrum of their associated linear differential operators has a finite-zone structure. The set of linear operators with a given finite-zone spectrum is the Jacobian variety of a Riemann surface, which is determined by the structure of the spectrum. We give an explicit solution of the corresponding non-linear equations in the language of the theory of Abelian functions.
@article{RM_1976_31_1_a2,
author = {B. A. Dubrovin and V. B. Matveev and S. P. Novikov},
title = {Non-linear equations of {Korteweg--de} {Vries} type, finite-zone linear},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {59--146},
publisher = {mathdoc},
volume = {31},
number = {1},
year = {1976},
language = {en},
url = {http://geodesic.mathdoc.fr/item/RM_1976_31_1_a2/}
}
TY - JOUR AU - B. A. Dubrovin AU - V. B. Matveev AU - S. P. Novikov TI - Non-linear equations of Korteweg--de Vries type, finite-zone linear JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 1976 SP - 59 EP - 146 VL - 31 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/RM_1976_31_1_a2/ LA - en ID - RM_1976_31_1_a2 ER -
%0 Journal Article %A B. A. Dubrovin %A V. B. Matveev %A S. P. Novikov %T Non-linear equations of Korteweg--de Vries type, finite-zone linear %J Trudy Matematicheskogo Instituta imeni V.A. Steklova %D 1976 %P 59-146 %V 31 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/RM_1976_31_1_a2/ %G en %F RM_1976_31_1_a2
B. A. Dubrovin; V. B. Matveev; S. P. Novikov. Non-linear equations of Korteweg--de Vries type, finite-zone linear. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 31 (1976) no. 1, pp. 59-146. http://geodesic.mathdoc.fr/item/RM_1976_31_1_a2/