INTEGRABILITY OF NON-LINEAR HAMILTONIAN-SYSTEMS BY INVERSE SCATTERING METHOD
INTEGRABILITY OF NON-LINEAR HAMILTONIAN-SYSTEMS BY INVERSE SCATTERING METHOD
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DOI：
10.1088/0031-8949/20/3-4/026
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发表时间：
1979-01-01
期刊：
影响因子：
2.9
通讯作者：
LIU, CS
中科院分区：
文献类型：
--
作者：
CHEN, HH;LEE, YC;LIU, CS
提出了一种用逆散射方法检验非线性发展方程可积性的简捷方法。逆散射变换所需的Lax方程的时间部分与原非线性Hamilton系统的线性化方程相一致，而Lax谱算子则与线性化方程的多项式解相联系的递归算子相一致。该谱算符是用微扰线性模耦合方法得到的。一个简单的例子被发现是可积的，我们的计划明确示出，以说明详细的程序。
A simple and direct scheme is presented to test the integrability of nonlinear evolution equations by inverse scattering method. The time part of the Lax equation needed for inverse scattering transform is identified with the linearized equation of the original nonlinear Hamiltonian system, while the Lax spectral operator is identified with a recursion operator connecting polynomial solutions of the linearized equation. This spectral operator is obtained by using a perturbative linear mode coupling scheme. A simple example discovered to be integrable by our scheme is shown explicitly to illustrate the detail procedures.