Far-Field Asymptotics for Multiple-Pole Solitons in the Large-Order Limit
Far-Field Asymptotics for Multiple-Pole Solitons in the Large-Order Limit
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DOI：
10.1016/j.jde.2021.06.016
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
Deniz Bilman;R. Buckingham;Deng‐Shan Wang
中科院分区：
文献类型：
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作者：
Deniz Bilman;R. Buckingham;Deng‐Shan Wang
可积聚焦的非线性薛定谔方程允许孤子解，其相关的谱数据由任意阶单对共轭极点组成。当极阶趋于无穷大时，我们研究了达布变换产生的这类多极孤子。我们证明了在适当的尺度下，在时空平面上有四个区域的解表现出定性不同的行为：指数衰减区、代数衰减区、非振荡区和振荡区。利用分析Riemann-Hilbert问题的非线性最速下降法，我们计算了在代数衰减区、非振荡区和振荡区的先导阶渐近行为。
The integrable focusing nonlinear Schrödinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by Darboux transformations as the pole order tends to infinity. We show that in an appropriate scaling, there are four regions in the space-time plane where solutions display qualitatively distinct behaviors: an exponential-decay region, an algebraic-decay region, a non-oscillatory region, and an oscillatory region. Using the nonlinear steepest-descent method for analyzing Riemann-Hilbert problems, we compute the leading-order asymptotic behavior in the algebraic-decay, non-oscillatory, and oscillatory regions.