Matter wave soliton solutions of the cubic-quintic nonlinear Schrödinger equation with an anharmonic potential

In this paper, the cubic-quintic nonlinear Schrödinger equation with an anharmonic potential is studied both analytically and numerically. As a result, two families of matter wave soliton solutions are obtained and their stability is analyzed by linear stability analysis and dynamical evolutions. It is shown that the spatially inhomogeneous cubic-quintic nonlinearities and the anharmonic potential can support stable matter wave solitons.