On the Whitham system for the radial nonlinear Schrödinger equation
On the Whitham system for the radial nonlinear Schrödinger equation
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DOI：
10.1111/sapm.12254
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发表时间：
2018-07
影响因子：
2.7
通讯作者：
M. Ablowitz;J. Cole;I. Rumanov
中科院分区：
文献类型：
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作者：
M. Ablowitz;J. Cole;I. Rumanov
研究了二维离焦径向非线性薛定谔（rNLS）方程的色散激波。这个方程在玻色-爱因斯坦凝聚、水波和非线性光学中自然出现。一个统一的非线性WKB方法，同样适用于可积或不可积偏微分方程，是用来找到rNLS Whitham调制方程系统的物理和流体动力学类型的变量。通过Whitham理论得到的描述DSW直接rNLS数值相比，结果表明非常好的定量协议。另一方面，正如预期的那样，与一维NLS方程的相应DSW解的比较显示出显着的定性和定量差异。
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schrödinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose‐Einstein condensates, water waves, and nonlinear optics. A unified nonlinear WKB approach, equally applicable to integrable or nonintegrable partial differential equations, is used to find the rNLS Whitham modulation equation system in both physical and hydrodynamic type variables. The description of DSWs obtained via Whitham theory is compared with direct rNLS numerics; the results demonstrate very good quantitative agreement. On the other hand, as expected, comparison with the corresponding DSW solutions of the one‐dimensional NLS equation exhibits significant qualitative and quantitative differences.