Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support.
Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support.
复制标题
DOI：
10.1103/physreve.53.1900
复制
发表时间：
1996-02
期刊：
影响因子：
--
通讯作者：
P. Olver;P. Rosenau
中科院分区：
文献类型：
--
作者：
P. Olver;P. Rosenau
一个简单的标度参数表明，大多数可积演化系统，这是已知的承认一个双哈密顿结构，是，事实上，由一个兼容的三重哈密顿结构。我们演示了他们的重组如何导致可积的层次结构赋予非线性色散，支持孤子（孤立波解决方案具有紧凑的支持），或尖和/或峰值孤子。通过构造修正的Korteweg\char21{}de弗里斯方程、非线性Schr\“odinger方程、用于模拟浅水波双向传播的可积Boussinesq系统和耦合非线性波动方程的Ito系统的对偶形式，说明了实现经典孤子和非光滑孤子之间对偶性的一般算法.这些阶层包括一个显着的各种有趣的可积非线性微分方程。\textcopyright{} 1996美国物理学会。
A simple scaling argument shows that most integrable evolutionary systems, which are known to admit a bi-Hamiltonian structure, are, in fact, governed by a compatible trio of Hamiltonian structures. We demonstrate how their recombination leads to integrable hierarchies endowed with nonlinear dispersion that supports compactons (solitary-wave solutions having compact support), or cusped and/or peaked solitons. A general algorithm for effecting this duality between classical solitons and their nonsmooth counterparts is illustrated by the construction of dual versions of the modified Korteweg\char21{}de Vries equation, the nonlinear Schr\"odinger equation, the integrable Boussinesq system used to model the two-way propagation of shallow water waves, and the Ito system of coupled nonlinear wave equations. These hierarchies include a remarkable variety of interesting integrable nonlinear differential equations. \textcopyright{} 1996 The American Physical Society.