On the Existence of Bright Solitons in Cubic-Quintic Nonlinear Schrödinger Equation with Inhomogeneous Nonlinearity

摘要

We give a proof of the existence of stationary bright soliton solutions of the cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity. Byusing bifurcation theory, we prove that the norm of the positive solution goes tozero as the parameterλ, called chemical potential in the Bose-Einsteincondensates' literature, tends to zero. Moreover, we solve the time-dependent cubic-quinticnonlinear Schrödinger equation with inhomogeneous nonlinearities by usinga numerical method.