双曲型非线性薛定谔方程的一个普遍渐近状态
A universal asymptotic regime in the hyperbolic nonlinear Schrödinger equation
摘要：
讨论了双空间一维双曲型非线性薛定谔（HNLS）方程基本长时间渐近区的出现。分析和广泛的数值模拟的基础上，一个近似的自相似的解决方案被发现在很大范围的初始条件-基本上为初始块的小到中等的能量。即使是相对较大的初始振幅，这意味着强非线性效应，最终导致局部结构类似的自相似的解决方案，适当的小修改。这些修改对于正确捕获解决方案阶段的行为非常重要。这个解决方案的一些方面表明，它是一个普遍的吸引子，从广泛的初始数据。
英文摘要：
The appearance of a fundamental long-time asymptotic regime in the two space one time dimensional hyperbolic nonlinear Schrödinger (HNLS) equation is discussed. Based on analytical and extensive numerical simulations an approximate self-similar solution is found for a wide range of initial conditions -- essentially for initial lumps of small to moderate energy. Even relatively large initial amplitudes, which imply strong nonlinear effects, eventually lead to local structures resembling those of the self-similar solution, with appropriate small modifications. These modifications are important in order to properly capture the behavior of the phase of the solution. This solution has aspects that suggest it is a universal attractor emanating from wide ranges of initial data.
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