|
ИСТИНА |
Войти в систему Регистрация |
Интеллектуальная Система Тематического Исследования НАукометрических данных |
||
Quasi-classical approach to the inverse scattering problem for the KdV equation, and solution of the Whitham modulation equationsстатья
Информация о цитировании статьи получена из
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 17 апреля 2024 г.
- Журнал: Theoretical and Mathematical Physics
- Том: 106
- Номер: 1
- Год издания: 1996
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 35
- Последняя страница: 49
- DOI: 10.1007/bf02070761
- Аннотация: We consider an initial value problem for the KdV equation in the limit of weak dispersion. This model describes the formation and evolution in time of a non-dissipative shock wave in plasma. Using the perturbation theory in power series of a small dispersion parameter, we arrive at the Riemann simple wave equation. Once the simple wave is overturned, we arrive at the system of Whitham modulation equations that describes the evolution of the resulting non-dissipative shock wave. The idea of the approach developed in this paper is to study the asymptotic behavior of the exact solution in the limit of weak dispersion, using the solution given by the inverse scattering problem technique. In the study of the problem, we use the WKB approach to the direct scattering problem and use the formulas for the exact multisoliton solution of the inverse scattering problem. By passing to the limit, we obtain a finite set of relations that connects the space-time parameters x, t and the modulation parameters of the non-dissipative shock wave.
- Добавил в систему: Мазур Николай Григорьевич