Asymptotic soliton train solutions of the defocusing nonlinear Schrödinger equation.
Asymptotic soliton train solutions of the defocusing nonlinear Schrödinger equation.
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离焦非线性薛定谔方程的渐近孤子列解。
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
B. Umarov
中科院分区：
文献类型：
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作者：
A. Kamchatnov;R. Kraenkel;B. Umarov
研究了初始“大而光滑”脉冲在由散焦非线性薛定谔方程控制的两个典型演化阶段的渐近行为。本文首先研究了小频散极限下的波浪破碎现象。对于无耗散激波在破波点后产生的情况，给出了Whitham调制方程的一个解。然后用半经典方法研究了由大而光滑的初始脉冲产生的渐近孤子串。由广义Bohr-Sommerfeld量子化规则计算了孤子串中沿着变化的参量，使得本征值的分布依赖于两个函数--初始脉冲的强度ρ（0）（x）和初始啁啾的增加ρ（0）（x）.研究了初始啁啾对系统渐近状态的影响。离焦NLS方程的数值解与渐近理论的预测非常吻合。
Asymptotic behavior of initially "large and smooth" pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrödinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Then, asymptotic soliton trains arising eventually from a large and smooth initial pulse are studied by means of a semiclassical method. The parameter varying along the soliton train is calculated from the generalized Bohr-Sommerfeld quantization rule, so that the distribution of eigenvalues depends on two functions-intensity rho(0)(x) of the initial pulse and its initial chirp upsilon(0)(x). The influence of the initial chirp on the asymptotic state is investigated. Excellent agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.