The Korteweg–De Vries Equation with Forcing Involving Products of Eigenfunctions
A new methodology has been recently introduced, which starting with an integrable evolution equation constructs an integrable forced version of this equation. The forcing consists of terms involving quadratic products of certain eigenfunctions of the associated Lax pair. We implement this methodolog...
Збережено в:
| Дата: | 2023 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Теми: | |
| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/998 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| Резюме: | A new methodology has been recently introduced, which starting with an integrable evolution equation constructs an integrable forced version of this equation. The forcing consists of terms involving quadratic products of certain eigenfunctions of the associated Lax pair. We implement this methodology starting with the celebrated Kortewg–de Vries equation. The initial value problem of the associated integrable forced equation can be formulated as a Riemann–Hilbert problem with a “jump matrix” that has explicit x and t dependence that can be computed in terms of the initial data. Thus, this equation can be solved as efficiently as the Kortewg–deVries equation itself. It is also shown that this forced equation together with the x-part of its Lax pair, appear in the modelling of important physical phenomena. Specifically, in the context of laser-plasma interaction, as well as in the description of resonant gravity-capillary waves.
Mathematical Subject Classification 2020: 37K10, 35B35, 35B34 |
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