Dressing for Fokker-Planck Equations: the Cases of $1+1$ and $1+\ell$ Dimensions
DOI:
https://doi.org/10.15407/mag19.02.503Анотація
Ми розглядаємо процедуру одягнення та явнi розв’язки скороченого скалярного рiвняння Фоккера–Планка у випадку розмiрностi $(1+1)$ i матричної системи Фоккера–Планка у випадку розмiрностi $(1+\ell)$. Для цього ми використовуємо наше узагальнене перетворення Беклунда–Дарбу (УПБД). Є лише декiлька праць щодо процедури одягнення для важливого рiвняння Фоккера–Планка i цi працi стосуються випадкiв розмiрностей $1+1$ та $1+2$.
Mathematical Subject Classification 2020: 35A30, 35Q84, 15A16
Ключові слова:
скорочене рiвняння Фоккера–Планка, матрична система Фоккера–Планка, процедура одягнення, перетворення Дарбу, матрична тотожнiсть, явний розв’язокПосилання
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