Tri-Hamiltonian Duality Between Solitons and Compactons
Tri-Hamiltonian Duality Between Solitons and Compactons
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发表时间：
1995
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通讯作者：
P. Olver;P. Rosenau
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作者：
P. Olver;P. Rosenau
一个简单的标度论证表明，大多数可积的演化系统，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。我们演示了如何重组，导致新的可积的层次赋予非线性色散，支持compactons，或尖和/或峰值孤子。通过构造修正的Korteweg-deVries方程、非线性Schr r odinger方程、用于模拟浅水波双向传播的可积Boussinesq方程组和耦合非线性波动方程的Ito方程组的对偶形式，给出了在经典孤子和非光滑孤子之间寻找这种新对偶的一般算法。这些新的层次包括一个显着的各种新的，有趣的可积非线性微分方程。
A simple scaling argument shows that most integrable evolutionary systems , which are known to admit a biHamiltonian structure, are, in fact, governed by a compatible trio of Hamiltonian structures. We demonstrate how their recombination leads to new integrable hierarchies endowed with nonlinear dispersion that supports com-pactons, or cusped and/or peaked solitons. A general algorithm for eeecting this new duality between classical solitons and their non-smooth counterparts is illustrated by the construction of dual versions of the modiied Korteweg-deVries equation, the nonlinear Schrr 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 new hierarchies include a remarkable variety of new, interesting integrable nonlinear diierential equations.