TY - JOUR
T1 - Large time asymptotics for the fourth-order nonlinear Schrödinger equation
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
N1 - Funding Information:
We would like to thank the unknown referee for useful comments and careful reading the first draft. The work of N.H. is supported by JSPS KAKENHI Grant Numbers 24654034 , 25220702 . The work of P.I.N. is partially supported by CONACYT and PAPIIT project IN100113 .
Publisher Copyright:
© 2014 Elsevier Inc.
PY - 2015/2/1
Y1 - 2015/2/1
N2 - We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation in the super critical case i∂tu+14∂x4u=λ∂x(|u|ρ-1u), where ρ. >. 4, λ. ∈. C. We prove the global existence and the large time asymptotics of solutions for small initial data u0∈H1∩H12,1, when the order of the nonlinearity ρ. >. 4.
AB - We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation in the super critical case i∂tu+14∂x4u=λ∂x(|u|ρ-1u), where ρ. >. 4, λ. ∈. C. We prove the global existence and the large time asymptotics of solutions for small initial data u0∈H1∩H12,1, when the order of the nonlinearity ρ. >. 4.
KW - Fourth-order nonlinear Schrödinger equation
KW - Large time asymptotics
UR - http://www.scopus.com/inward/record.url?scp=84919478689&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84919478689&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2014.10.007
DO - 10.1016/j.jde.2014.10.007
M3 - Article
AN - SCOPUS:84919478689
SN - 0022-0396
VL - 258
SP - 880
EP - 905
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 3
ER -