The semiclassical limit of the nonlinear Schrodinger equation in a radial potential

In this paper, we are concerned with the following nonlinear Schrodinger equation: ihpartial derivativepsi/partial derivativet = -h(2)/2m Deltapsi + V(x)psi - gamma(h)\psi\(p-2)psi, gamma(h) > 0, x is an element of R-2, where h > 0, 2 < p < 6, psi : R-2 --> C, and the potential V is radially symmetric, Our main purpose is to obtain positive solutions among the functions having the form psi(r, theta, t) = exp(iM(h)theta/h + iEt/h)v(r), being r, theta the polar coordinates in the plane. Since we assume M-h > 0, the functions in this special class have nontrivial angular momentum as it will be specified in the Introduction. Furthermore. our solutions exhibit a spike-layer pattern when the parameter h approaches zero our object is to analyse the appearance of such type of concentration asymptotic behaviour in order to locate the asymptotic peaks. (C) 2002 Elsevier Science (USA).