Нелiнiйне рiвняння Шредiнґера вищого порядку для обвiдної повiльно модульованих гравiтацiйних хвиль на поверхнi рiдини скiнченної глибини та його квазiсолiтоннi розв’язки
We consider the high-order nonlinear Schrödinger equation derived earlier by Sedletsky [Ukr. J. Phys. 48(1), 82 (2003)] for the first-harmonic envelope of slowly modulated gravity waves on the surface of finite-depth irrotational, inviscid, and incompressible fluid with flat bottom. This equation ta...
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| Дата: | 2014 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English Ukrainian |
| Опубліковано: |
Publishing house "Academperiodika"
2014
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| Теми: | |
| Онлайн доступ: | https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2018565 |
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| Назва журналу: | Ukrainian Journal of Physics |
Репозитарії
Ukrainian Journal of Physics| Резюме: | We consider the high-order nonlinear Schrödinger equation derived earlier by Sedletsky [Ukr. J. Phys. 48(1), 82 (2003)] for the first-harmonic envelope of slowly modulated gravity waves on the surface of finite-depth irrotational, inviscid, and incompressible fluid with flat bottom. This equation takes into account the third-order dispersion and cubic nonlinear dispersive terms. We rewrite this equation in dimensionless form featuring only one dimensionless parameter kℎ, where k is the carrier wavenumber and ℎ is the undisturbed fluid depth. We show that one-soliton solutions of the classical nonlinear Schrödinger equation are transformed into quasi-soliton solutions with slowly varying amplitude when the high-order terms are taken into consideration. These quasi-soliton solutions represent the secondary modulations of gravity waves. |
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