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

作者：Hayashi Nakao^*; Kaikina Elena I

来源：Mathematical Methods in the Applied Sciences, 2017, 40(5): 1573-1597.

DOI：10.1002/mma.4080

• Third-order nonlinear Schrodinger equation
• large time asymptotics

We consider the Cauchy problem for the third-order nonlinear Schrodinger equation
{i partial derivative(t)u - 1/3 H partial derivative(3)(x)u = lambda vertical bar u vertical bar(3) u, (t,x) is an element of R+ x R,
u (0,x) = u(0) (x) , x is an element of R, ( 1)
where H = F(-1)i xi vertical bar xi vertical bar(-1) F and F is the Fourier transform. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions for the defocusing case lambda > 0 with a logarithmic correction under the non zero mass condition integral u(0) (x) dx not equal 0.

• 出版日期2017-3-30