论文标题
通过非线性schrödinger方程的弱非局部散落的通用减少和孤立波
Universal reductions and solitary waves of weakly nonlocal defocusing nonlinear Schrödinger equations
论文作者
论文摘要
我们研究了弱非局部散落的非线性schrödinger（NLS）模型的渐近减少和孤立波。通过多尺度扩展方法分析后者的流体动力形式。对于近似的领先（仅存在响应函数的第一刻），我们表明，以深色孤子形式的孤立波由有效的Boussinesq/Benney-Luke（BBL）方程来控制，该方程描述了浅水中的双向波。然后，很长时间以来，我们将BBL方程式减少为右波和左波波的一对Korteweg-de Vries（KDV）方程，并表明BBL孤立波转换为KDV Soliton。此外，对于下一个近似顺序（其中存在响应函数的第一刻和第二矩），我们发现暗孤子受到高阶扰动KDV（PKDV）方程的控制，该方程已用于描述在较高效应的情况下等离子体和水波中的离子声音孤子。 PKDV方程是通过高阶集成系统近似的，因此，仅发现孤子形状和速度的不变变化，而没有产生辐射尾巴（在此有效的KDV图片中）。
We study asymptotic reductions and solitary waves of a weakly nonlocal defocusing nonlinear Schrödinger (NLS) model. The hydrodynamic form of the latter is analyzed by means of multiscale expansion methods. To the leading-order of approximation (where only the first moment of the response function is present), we show that solitary waves, in the form of dark solitons, are governed by an effective Boussinesq/Benney- Luke (BBL) equation, which describes bidirectional waves in shallow water. Then, for long times, we reduce the BBL equation to a pair of Korteweg-de Vries (KdV) equations for right- and left-going waves, and show that the BBL solitary wave transforms into a KdV soliton. In addition, to the next order of approximation (where both the first and second moment of the response function are present), we find that dark solitons are governed by a higher-order perturbed KdV (pKdV) equation, which has been used to describe ion-acoustic solitons in plasmas and water waves in the presence of higherorder effects. The pKdV equation is approximated by a higher-order integrable system and, as a result, only insubstantial changes in the soliton shape and velocity are found, while no radiation tails (in this effective KdV picture) are produced.
