Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 935390, 14 pages
doi:10.1155/2008/935390
Abstract
We give a proof of the existence of stationary bright soliton solutions of the
cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity. By
using bifurcation theory, we prove that the norm of the positive solution goes to
zero as the parameter λ, called chemical potential
in the Bose-Einstein
condensates' literature, tends to zero. Moreover, we solve the time-dependent cubic-quintic
nonlinear Schrödinger equation with inhomogeneous nonlinearities by using
a numerical method.