Type: Article

Large Time Asymptotics for the Kadomtsev–Petviashvili Equation

Hayashi, Nakao; Naumkin, Pavel I.;

Abstract:

We study the large time asymptotic behavior of solutions to the Kadomtsev–Petviashvili equations {ut+uxxx+???1xuyy=??xu2,(x,y)?R2,t?R,u(0,x,y)=u0(x,y),(x,y)?R2, where ? = ±1 and ??1x=?x??dx? . We prove that the large time asymptotics of the derivative u x of the solution has a quasilinear character.