Three-dimensional rogue waves in nonstationary parabolic potentials.
Three-dimensional rogue waves in nonstationary parabolic potentials.
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DOI：
10.1103/physreve.82.036610
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
Zhenya Yan;V. Konotop;N. Akhmediev
中科院分区：
文献类型：
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作者：
Zhenya Yan;V. Konotop;N. Akhmediev
利用对称性分析，系统地给出了一个高维相似变换，将具有抛物势的变系数（3+1）维非齐次非线性薛定谔（NLS）方程化为常系数（1+1）维NLS方程.这种变换使我们能够将（3+1）维情形的某些局部化精确解与（1+1）维情形的可积NLS方程的各种解联系起来。作为一个例子，我们说明了我们的技术，使用两个最低阶的合理的解决方案的NLS方程作为播种功能，以获得流氓wavelike解决方案，本地化在三维空间中，有复杂的演变，包括两个时间依赖流氓波解决方案之间的相互作用。所得的三维反常波解为相关实验的开展和在非线性光学和玻色-爱因斯坦凝聚体中的应用提供了可能。
Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1) -dimensional inhomogeneous nonlinear Schrödinger (NLS) equation with variable coefficients and parabolic potential to the (1+1) -dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1) -dimensional case to the variety of solutions of integrable NLS equation of the (1+1) -dimensional case. As an example, we illustrated our technique using two lowest-order rational solutions of the NLS equation as seeding functions to obtain rogue wavelike solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wavelike solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and Bose-Einstein condensates.