Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
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DOI：
10.1088/0266-5611/17/4/329
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发表时间：
2001
期刊：
影响因子：
2.1
通讯作者：
Mark S Alber;Yuri N Fedorov
中科院分区：
文献类型：
--
作者：
Mark S Alber;Yuri N Fedorov
结合超椭圆Jacobian的非线性子簇上的Hamilton流，研究了一个新的浅水方程和Dym型方程的代数几何解.这些方程属于一类由Lax方程生成的N分量可积系统，其能量依赖的薛定谔算子在谱参数中具有极点。这些方程的类的准周期和孤子型解描述的θ和τ函数，通过使用新的参数化。实值解的定性描述。
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 Schrödinger 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.