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math.AP2022★ 2 cited
The generalized fractional KdV equation in weighted Sobolev spaces
Alysson Cunha, Oscar Riaño
This work concerns the study of persistence property in polynomial weighted spaces for solutions of the generalized fractional KdV equation in any spatial dimension . By e…
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…