A Simple model of the integrable Hamiltonian equation
A Simple model of the integrable Hamiltonian equation
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DOI：
10.1063/1.523777
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发表时间：
1978-05
影响因子：
1.3
通讯作者：
F. Magri
中科院分区：
文献类型：
--
作者：
F. Magri
本文提出了一种分析无限维哈密顿方程的方法，该方法避免了引入Backlund变换或使用Lax方程。这种分析是基于可能性连接在几个方面的特殊哈密顿方程的守恒律与它们的对称性，通过使用辛算子。它导致了一个简单而足够普遍的可积哈密顿方程模型，其中Korteweg-de弗里斯方程，修正的Korteweg-de弗里斯方程，非线性薛定谔方程和所谓的Harry Dym方程是其特例。
A method of analysis of the infinite‐dimensional Hamiltonian equations which avoids the introduction of the Backlund transformation or the use of the Lax equation is suggested. This analysis is based on the possibility of connecting in several ways the conservation laws of special Hamiltonian equations with their symmetries by using symplectic operators. It leads to a simple and sufficiently general model of integrable Hamiltonian equation, of which the Korteweg–de Vries equation, the modified Korteweg–de Vries equation, the nonlinear Schrodinger equation and the so‐called Harry Dym equation turn out to be particular examples.