Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.
Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.
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DOI：
10.1103/physreve.80.036607
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
Zhenya Yan;Zhenya Yan;V. Konotop
中科院分区：
文献类型：
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作者：
Zhenya Yan;Zhenya Yan;V. Konotop
结果表明，利用相似变换，一组具有非齐次系数的三维p-q非线性薛定谔（NLS）方程可以化为具有常系数或变系数的一维定常NLS方程，从而可以得到精确的局域波解和周期波解.该方法将（1+3）空间中的原始坐标映射为一组单参数坐标曲面，其参数起着一维方程坐标的作用。我们描述的算法，寻找解决方案，并集中在电源（线性和非线性）的潜力，提出了一些案例。本文还讨论了该方法的推广。
It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the (1+3) space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.