We consider the Cauchy problem for the higher-order nonlinear Schro¨dinger equation
(0.1) i∂tu + 1/2∂2xu - 1/4∂4xu = u3,t>0,x∈R
u(0,x) = u0(x), x∈R.
The aim of the present paper is prove the global existence of solutions to (0.1) if the initial data u0 ∈ H1 ∩ H0,1. Also we find the large time asymptotics of solutions.
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