Open AccessСentrosymmetric Solitons with Power Asymptotics for Media of Different Dimensions
Author(s) -
A. D. Suprun,
Л. В. Шмелева
Publication year - 2018
Publication title -
ukrainian journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.213
H-Index - 17
eISSN - 2071-0194
pISSN - 2071-0186
DOI - 10.15407/ujpe63.10.924
Subject(s) - infinity , nonlinear system , space (punctuation) , mathematical analysis , mathematics , range (aeronautics) , power (physics) , term (time) , physics , quantum mechanics , computer science , materials science , composite material , operating system
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.