Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media
Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media
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DOI：
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发表时间：
1970
影响因子：
1.1
通讯作者：
V. Zakharov;A. Shabat
中科院分区：
文献类型：
--
作者：
V. Zakharov;A. Shabat
证明了描述平面自聚焦和一维自调制的方程Iol/J/ot+L/Jxx+K1+12 1/1=0可以归结为某个线性微分算子的逆散射问题来精确求解。在这种情况下，可以得到描述孤立波包--孤子相互作用的精确解。结果表明，相互作用孤子的振幅和速度不变，而位相存在不连续性。结果还表明，只有成对的孤子发生碰撞。所得结果用于评估自调制不稳定性发展的非线性阶段。
It is demonstrated that the equation iol/J/ot + l/Jxx + K 1¢12 1/1 = 0, which describes plane self-focusing and one-dimensional self-modulation can be solved exactly by reducing it to the inverse scattering problem for a certain linear differential operator. In this case exact solutions can be obtained which describe the interaction of solitary wave packets--solitons. It is shown that the amplitude and velocity of interacting solitons do not change, whereas the phase has a discontinuity. It is also demonstrated that only paired collisions of solitons occur. The results obtained are used for assessing the nonlinear stage of development of self-modulated instability.