Large Time Asymptotics for the Kadomtsev-Petviashvili Equation

作者：Hayashi Nakao^*; Naumkin Pavel I

来源：Communications in Mathematical Physics, 2014, 332(2): 505-533.

DOI：10.1007/s00220-014-2159-x

We study the large time asymptotic behavior of solutions to the Kadomtsev-Petviashvili equations %26lt;br%26gt;{u(t) + u(xxx) + sigma partial derivative(-1)(x) u(yy) = -partial derivative(x)u(2), (x,y) is an element of R-2, t is an element of R {u (0, x, y) = u(0) (x, y), (x,y) is an element of R-2, %26lt;br%26gt;where sigma = +/- 1 and partial derivative(-1)(x) = integral(x)(-infinity) dx%26apos;. We prove that the large time asymptotics of the derivative u(x) of the solution has a quasilinear character.

• 出版日期2014-12