Stability of line solitons for the KP-II equation
The KP-II equation was derived by Kadmotsev and Petviashvili to explain stability of line solitary waves of shallow water. In this talk, I will show stability of $1$-line solitons for perturbations in the class $(1+x^2)^{-1/2-0}H^1(\mathbb{R}_{x,y}^2)$