The Three-Wave Interaction-A Nondispersive Phenomenon
The Three-Wave Interaction-A Nondispersive Phenomenon
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DOI：
10.1002/sapm19765519
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发表时间：
1976-03
影响因子：
2.7
通讯作者：
D. Kaup
中科院分区：
文献类型：
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作者：
D. Kaup
对于有界包络，三波共振相互作用的一维形式可以通过反散射变换精确求解，这最初是由Zakharov和Manakov提出的。除了解决三阶逆散射问题，我们还展示了如何用三个简单的二阶问题来解决这个更复杂的三阶三波问题。一般的结果是，在相互作用期间，包含在具有中间群速度的波的包络中的所有孤子将“分裂”，并且被添加到包含在快包络和慢包络中的孤子的原始数目。然后将这些结果应用于等离子体的“衰变”和“爆炸”不稳定性，得到了在ft →+∞的渐近极限激发爆炸不稳定性的充要条件。
The one‐dimensional form of the three‐wave resonant interaction, for bounded envelopes, is solved exactly by an inverse scattering transform, which was originally suggested by Zakharov and Manakov. In addition to solving a third‐order inverse scattering problem, we show how to solve this more complicated third‐order three‐wave problem in terms of three simpler second‐order problems. The general result is that during the interaction, all solitons contained in the envelope of the wave with the middle group velocity will “split,” and be added to the original number of solitons contained in both the fast and slow envelopes. These results are then applied to the “decay” and “explosive” instabilities of plasmas, and necessary and sufficient conditions are found for exciting the explosive instability in the asymptotic limit oft→+∞.