Центрально-симетричні солітони зі ступеневою асимптотикою для середовищ різної розмірності
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 so...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English Ukrainian |
| Published: |
Publishing house "Academperiodika"
2018
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| Subjects: | |
| Online Access: | https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2018022 |
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| Journal Title: | Ukrainian Journal of Physics |
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Ukrainian Journal of Physics| Summary: | 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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