Global well-posedness and long-time asymptotics for the defocussing Davey-Stewartson II equation in \(H^{1,1}(\mathbb{C})\) (Q329697)

The \(\bar{\partial}\)-inverse scattering method is used to obtain global well-posedness and large-time asymptotics for the defocussing Davey-Stewartson II equation NEWLINE\[NEWLINE\begin{aligned} iu_t+2({\bar{\partial}}^2+ {{\partial}}^2)u+(g+\bar g)u&=0, \\ {\bar{\partial}}g+{{\partial}}(| u|^2)&=0.\end{aligned} NEWLINE\]NEWLINE These global solutions are dispersive by computing their leading asymptotic behavior as \(t\to\infty\) in terms of an associated linear problem. Results are sharp.