关于双周期波在横向上的变化
On the variation of of bi-periodic waves in the transverse direction
摘要：
在实验室中产生在x方向上传播且在y方向上振幅变化的波的双周期图案。在矢量（vNLSE）和标量（sNLSE）的非线性薛定谔方程的框架内，使用的vNLSE和Jacobi椭圆正弦函数的解的一致振幅，Stokes式的解决方案的sNLSE的振幅变化的研究。波列是使用vNLSE的类斯托克斯解生成的;然而，两种预测的比较表明，虽然它们都能很好地预测观测到的y振幅变化，但与sNLSE的椭圆函数解的比较误差要小得多。此外，为了与vNLSE解一致，必须包括来自相互作用的对称波列的斯托克斯型展开的y项中的三次谐波。没有证据表明不稳定性在x方向上增长，这与Segur及其同事的工作一致，他们表明耗散稳定了调制不稳定性。在y中存在一些额外的振幅变化，这通过允许在该方向上对称性破缺的定性稳定性计算来检查。
英文摘要：
Bi-periodic patterns of waves that propagate in the x direction with amplitude variation in the y direction are generated in a laboratory. The amplitude variation in the y direction is studied within the framework of the vector (vNLSE) and scalar (sNLSE) nonlinear Schrodinger equations using the uniform-amplitude, Stokes-like solution of the vNLSE and the Jacobi elliptic sine function solution of the sNLSE. The wavetrains are generated using the Stokes-like solution of vNLSE; however, a comparison of both predictions shows that while they both do a reasonably good job of predicting the observed amplitude variation in y, the comparison with the elliptic function solution of the sNLSE has significantly less error. Additionally, for agreement with the vNLSE solution, a third harmonic in y term from a Stokes-type expansion of interacting, symmetric wavetrains must be included. There is no evidence of instability growth in the x-direction, consistent with the work of Segur and colleagues, who showed that dissipation stabilizes the modulational instability. There is some extra amplitude variation in y, which is examined via a qualitative stability calculation that allows symmetry breaking in that direction.
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