Nonisospectral scattering problems: A key to integrable hierarchies
Nonisospectral scattering problems: A key to integrable hierarchies
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DOI：
10.1063/1.533055
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发表时间：
1999-11-01
影响因子：
1.3
通讯作者：
Pickering, A
中科院分区：
文献类型：
--
作者：
Gordoa, PR;Pickering, A
我们发现，某些偏微分方程在2+1维的非等谱散射问题提供了一个关键的相关可积的常微分方程和偏微分方程的层次。这说明使用（一个扩展）一个已知的二阶和两个新的三阶非等谱散射问题。这些散射问题使我们能够得到新的层次的可积偏微分方程，在1+1和2+1维，连同其基本的线性问题（isospectral和nonisospectral）;和新的层次的可积常微分方程，再次与其基本的线性问题。(C)1999年美国物理学会。[S0022-2488（99）04210-3]。
We show that certain partial differential equations associated to nonisospectral scattering problems in 2+1 dimensions provide a key to associated integrable hierarchies of both ordinary and partial differential equations. This is illustrated using (an extension of) a known second-order and two new third-order nonisospectral scattering problems. These scattering problems allow us to derive new hierarchies of integrable partial differential equations, in both 1+1 and 2+1 dimensions, together with their underlying linear problems (isospectral and nonisospectral); and also new hierarchies of integrable ordinary differential equations, again with their underlying linear problems. (C) 1999 American Institute of Physics. [S0022-2488(99)04210-3].