Note on Asymptotic Solutions of the Korteweg‐de Vries Equation with Solitons
Note on Asymptotic Solutions of the Korteweg‐de Vries Equation with Solitons
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关于带孤子的 Korteweg‐de Vries 方程渐近解的注记
DOI：
10.1002/sapm1982662159
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发表时间：
1982
影响因子：
2.7
通讯作者：
Y. Kodama
中科院分区：
文献类型：
--
作者：
M. Ablowitz;Y. Kodama
描述了包含孤子和色散波列的Korteweg - de - Vries方程的长时间渐近解。结果表明，孤子不仅与色散波串有弹性相互作用，而且与其他孤子也有弹性相互作用。给出了相互作用产生相移的显式公式。这些思想也适用于其他由逆散射变换可解的非线性演化方程。
The long time asymptotic solution of the Korteweg‐de Vries equation containing both solitons and the dispersive wavetrain is described. It is shown that a soliton interacts elastically both with the dispersive wavetrain and with other solitons. An explicit formula for the phase shift produced upon interaction is given. These ideas also apply to other nonlinear evolution equations solvable by the inverse scattering transform.