Instabilities in the two-dimensional cubic nonlinear Schrödinger equation.
Instabilities in the two-dimensional cubic nonlinear Schrödinger equation.
复制标题
二维三次非线性薛定谔方程的不稳定性。
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
H. Segur
中科院分区：
文献类型：
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作者：
J. Carter;H. Segur
二维立方非线性薛定谔方程（NLS）可以用作从深水中的波到光纤中的脉冲的物理系统中的现象的模型。本文证明了具有线性相位的非线性最小二乘方程的一维行波解对于具有二维结构的无穷小扰动是不稳定的。如果线性色散项的系数具有相同的符号（椭圆情况），则仅有的不稳定扰动具有比明确定义的截止更长的横向波长。如果线性色散项的系数具有相反的符号（双曲线情况），则不存在这种截止，并且随着波长减小，最大增长率接近明确定义的极限。
The two-dimensional cubic nonlinear Schrödinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional traveling wave solution of NLS with linear phase is unstable with respect to some infinitesimal perturbation with two-dimensional structure. If the coefficients of the linear dispersion terms have the same sign (elliptic case), then the only unstable perturbations have transverse wavelength longer than a well-defined cutoff. If the coefficients of the linear dispersion terms have opposite signs (hyperbolic case), then there is no such cutoff and as the wavelength decreases, the maximum growth rate approaches a well-defined limit.