нелинейные уравнения волнового типа (уравнения Шредингера, Кортевега-де Фриза, Захарова-Кузнецова, и т.д.), изучение локальных и глобальных решений и свойств
Основные публикации:
Klein, Christian; Roudenko, Svetlana; Stoilov, Nikola, “Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation”, Physica D, 423 (2021), 132913
Roudenko, Svetlana; Wang, Zhongming; Yang, Kai, “Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study.”, Journal of Computational Physics, 445 (2021), 110570
Campos, Luccas; Farah, Luiz Gustavo; Roudenko, Svetlana, “Threshold solutions for the nonlinear Schrödinger equation”, Revista Matemática Iberoamericana, 38:5 (2022), 1637-1708
Landoulsi, Oussama; Roudenko, Svetlana; Yang, Kai, “Interaction with an obstacle in the 2D focusing nonlinear Schrödinger equation”, Advances in Computational Mathematics, 49:5 (2023), 71
Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana; Yang, Kai, “Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation”, American Journal of Mathematics, 145:6 (2023), 1695–775
