Asymptotics for the fourth-order nonlinear Schrodinger equation in the critical case

作者：Hayashi Nakao^*; Mendez Navarro Jesus A; Naumkin Pavel I

来源：Journal of Differential Equations, 2016, 261(9): 5144-5179.

DOI：10.1016/j.jde.2016.07.026

• Fourth-order nonlinear Schrodinger equation
• Large time asymptotics

We consider the Cauchy problem for the fourth-order nonlinear Schrodinger equation
{i partial derivative(t)u - 1/4 partial derivative(4)(x)u = lambda vertical bar u vertical bar(4)u, (t,x) is an element of R+ x R, u(0,x) = u(0) (x) , x is an element of R.
We prove the large time asymptotic behavior of solutions with a logarithmic correction under the conditions integral u(0) (x)dx not equal 0, lambda > 0.

• 出版日期2016-11-5