关于非线性光学中的Madelung系统：一种倒易不变性
On Madelung systems in nonlinear optics: A reciprocal invariance
摘要：
德布罗意玻姆势的作用，最初被建立为中心的玻姆量子力学，检查两个典型的马德隆系统在非线性光学。在一个开创性的情况下，由瓦格纳等人。通过傍轴近似，其中的德布罗意-玻姆势是目前的Madelung系统，示出承认多参数类这里引入的“q-高斯”。在Tsallis参数q> 1的极限下，q-高斯子将导致标准的高斯孤子，这是封装Madelung系统的对数非线性Schroedinger方程所承认的。对于具有双幂律折射率的光学介质，得到了q-高斯。在第二种情况下，最初通过程函近似的激光束传播的背景下，其中德布罗意玻姆项被忽略的Madelung系统，承认下一类新的双参数互易变换的不变性。介绍了类似于经典气体动力学中著名的卡门-钱氏定律的模型光学定律。
英文摘要：
The role of the de Broglie-Bohm potential, originally established as central to Bohmian quantum mechanics, is examined for two canonical Madelung systems in nonlinear optics. In a seminal case, a Madelung system derived by Wagner et al. via the paraxial approximation and in which the de Broglie-Bohm potential is present, is shown to admit a multi-parameter class of what are here introduced as "q-gaussons". In the limit as the Tsallis parameter q --> 1, the q-gaussons are shown to lead to standard gausson solitons as admitted by logarithmic nonlinear Schroedinger equation encapsulating the Madelung system. The q-gaussons are obtained for optical media with dual power-law refractive index. In the second case, a Madelung system originally derived via an eikonal approximation in the context of laser beam propagation and in which the de Broglie Bohm term is neglected, is shown to admit invariance under a novel class of two-parameter reciprocal transformations. Model optical laws analogous to the celebrated Karman-Tsien law of classical gasdynamics are introduced.
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