Journal of Physical Studies 8(2), 137–140 (2004) DOI: https://doi.org/10.30970/jps.08.137 THREE-DIMENSIONAL SOLUTIONS IN MEDIA WITH SPATIAL DEPENDENCE OF NONLINEAR REFRACTIVE INDEX L. M. Kovachev, N. I. Kaymakanova1, D. Y. Dakova1, L. I. Pavlov2, R. A. Rousev2, S. G. Donev2, R. L. Pavlov2 Institute of Electronics, Bulgarian Academy of Sciences, Tsarigradcko Chaussee 72,1784 Sofia, Bulgaria, 1Plovdiv University, 24 Tsar Asen Str., 4000 Plovdiv,Bulgaria, 2Institute for Nuclear Research and Nuclear Energy, 72 Tsarigradsko Chaussee, 1784, Bulgaria

We investigate a nonparaxial vector generalization of the scalar 3D+1 Nonlinear Schr{ödinger Equation (NSE). In spherical presentation it is possible to reduce this equation to usual scalar Nonlinear Schr{ödinger Equation in respect to $t,r=\sqrt{x^2+y^2+z^2}$ coordinates. Thus, all periodical and solitary solutions of the NSE will generate 3D+1 vector solitons. Such reduction is possible only when the spatial dependence of the nonlinear refractive index is of the type of $n_2\cong(x^2+y^2)χ^{(3)}/r_0$. Exact analytical 3D+1 soliton solutions are obtained for the first time in media of spatial dependance of the nonlinear refractive index.

PACS number(s): 42.81.Dp, 05.45.Yv, 42.65.Tg

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