Dissipative character of asymptotics for the nonlinear fractional Schrodinger equation

We consider the Cauchy problem for the fractional nonlinear Schrodinger equation i partial derivative(t)u + 2/5 vertical bar partial derivative(x)vertical bar(5/2) u = lambda vertical bar u vertical bar(5/2) u, where lambda is an element of R. We obtain the large time asymptotic behavior of solutions, which has a self-similar behavior and a logarithmic modification compared with the corresponding linear problem. Published under license by AIP Publishing.