Large Time Behavior for the Cubic Nonlinear Schrödinger Equation
2002 ◽
Vol 54
(5)
◽
pp. 1065-1085
◽
Keyword(s):
AbstractWe consider the Cauchy problem for the cubic nonlinear Schrödinger equation in one space dimensionCubic type nonlinearities in one space dimension heuristically appear to be critical for large time. We study the global existence and large time asymptotic behavior of solutions to the Cauchy problem (1). We prove that if the initial data are small and such that for some n ∈ Z, and , then the solution has an additional logarithmic timedecay in the short range region . In the far region the asymptotics have a quasilinear character.
2000 ◽
Vol 130
(5)
◽
pp. 1029-1043
◽
1998 ◽
Vol 50
(4)
◽
pp. 1015-1026
2016 ◽
Vol 18
(03)
◽
pp. 1550035
◽