Сentrosymmetric Solitons with Power Asymptotics for Media of Different Dimensions


  • A. D. Suprun Taras Shevchenko National University of Kyiv
  • L. V. Shmeleva Taras Shevchenko National University of Kyiv




сentrosymmetric solitons, nonlinear Schr¨odinger equation, graphene


Analytic solutions of radially symmetric nonlinear Schr¨odinger equations with two nonlinear terms with different powers are analyzed for 1D, 2D, and 3D spaces. They are typical of the equations, where there are two nonlinear terms instead of one cubic term, as a rule. An important feature of the solutions obtained is that they are expressed not in terms of hyperbolic functions, but in terms of rational functions finite in the entire space with a power asymptotics at infinity. The solutions obtained significantly expand the range of applications of the nonlinear Schr¨odinger equations. Separate relevant cases of the general solution are considered in the applications.


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How to Cite

Suprun, A. D., & Shmeleva, L. V. (2018). Сentrosymmetric Solitons with Power Asymptotics for Media of Different Dimensions. Ukrainian Journal of Physics, 63(10), 924. https://doi.org/10.15407/ujpe63.10.924



Semiconductors and dielectrics