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math.AP2022
Threshold solutions for the Hartree equation
Anudeep K. Arora, Svetlana Roudenko
We consider the focusing d Hartree equation, which is -supercritical, with finite energy initial data, and investigate the solutions at the mass-energy threshold. We establ…
math.AP2022★ 3 cited
Stability and instability of solitary waves in fractional generalized KdV equation in all dimensions
Oscar Riaño, Svetlana Roudenko
We study stability of solitary wave solutions for the fractional generalized Korteweg-de Vries equation $$ \partial_t u- \partial_{x_1} D^αu+ \tfrac{1}{m}\partial_{x_1}(u^m)=0, ~ (…
math.AP2022★ 8 cited
Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity
Isaac Friedman, Oscar Riaño, Svetlana Roudenko +2
We consider two types of the generalized Korteweg - de Vries equation, where the nonlinearity is given with or without absolute values, and, in particular, including the low powers…