We consider the critical Korteweg–de Vries (KdV) equation: Let () be soliton solutions to this equation. Denote the KdV linear group, and let be with sufficient decay on the right; that is, let be for some .
We construct a solution to the critical KdV equation such that
"Construction of solutions to the -critical KdV equation with a given asymptotic behaviour." Duke Math. J. 138 (3) 487 - 531, 15 June 2007. https://doi.org/10.1215/S0012-7094-07-13835-3