TY - JOUR
T1 - Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case
AU - Hayashi, Nakao
AU - Mendez-Navarro, Jesus A.
AU - Naumkin, Pavel I.
N1 - Funding Information:
The work of N.H. is partially supported by JSPS KAKENHI Grant Numbers JP25220702 , JP15H03630 . The work of P.I.N. is partially supported by CONACYT and PAPIIT project IN100616 .
PY - 2016/11/5
Y1 - 2016/11/5
N2 - We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation{i∂tu−14∂x4u=λ|u|4u, (t,x)∈R+×R,u(0,x)=u0(x), x∈R. We prove the large time asymptotic behavior of solutions with a logarithmic correction under the conditions ∫u0(x)dx≠0, λ>0.
AB - We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation{i∂tu−14∂x4u=λ|u|4u, (t,x)∈R+×R,u(0,x)=u0(x), x∈R. We prove the large time asymptotic behavior of solutions with a logarithmic correction under the conditions ∫u0(x)dx≠0, λ>0.
KW - Fourth-order nonlinear Schrödinger equation
KW - Large time asymptotics
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U2 - 10.1016/j.jde.2016.07.026
DO - 10.1016/j.jde.2016.07.026
M3 - Article
AN - SCOPUS:84992035486
VL - 261
SP - 5144
EP - 5179
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 9
ER -