任意锐减初始脉冲下一维孤立子方程散射数据的逼近方法
An Approximation Method for the Scattering Data of One-Dimensional Soliton Equations under Arbitrary Rapidly-Decreasing Initial Pulses
摘要：
我们提出了一种新的近似方法，可以预测在任意快速减少的初始波包下渐近出现的孤子数。在不对原孤子方程进行积分的情况下，可以估计出孤子的数目。以一维非线性薛定谔方程为例，详细估计了散射振幅的行为。结果表明，与直接数值积分得到的结果吻合良好。所提出的方法适用于广泛的一类一维孤子方程。
英文摘要：
We present a novel approximation method that can predict the number of solitons asymptotically appearing under arbitrary rapidly decreasing initial wave packets. The number of solitons can be estimated without integration of the original soliton equations. As an example, we take the one-dimensional nonlinear Schrodinger equation and estimate the behaviors of the scattering amplitude in detail. The results show good agreement compared with those obtained by direct numerical integration. The presented method is applicable to a wide class of one-dimensional soliton equations.
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