Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians

被引：64
作者：
Alber, MS
Fedorov, YN
机构：
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA
[3] Moscow MV Lomonosov State Univ, Dept Math & Mech, Moscow 119899, Russia
来源：
INVERSE PROBLEMS | 2001年 / 17卷 / 04期
关键词：
D O I：
10.1088/0266-5611/17/4/329
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Algebraic geometrical solutions of a new shallow-water equation and Dym-type equation are studied in connection with Hamiltonian flows on nonlinear subvarieties of hyperelliptic Jacobians. These equations belong to a class of N-component integrable systems generated by Lax equations with energy-dependent Schrodinger operators having poles in the spectral parameter. The classes of quasi-periodic and soliton-type solutions of these equations are described in terms of theta- and tau-functions by using new parametrizations. A qualitative description of real-valued solutions is provided.
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页码：1017 / 1042
页数：26
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