Soliton solutions of cubic–quintic nonlinear Schrödinger equation with combined time-dependent magnetic–optical potentials

We investigate the explicit matter-wave soliton solutions of the cubic–quintic nonlinear Schrödinger equation with spatiotemporal modulation of the nonlinearities and potentials. With a systematic way, we construct some integrable systems with localized cubic–quintic nonlinearities and an infinite number of potentials, including optical lattice potential and combined time-dependent magnetic–optical potentials in the form of linear–lattice, harmonic–lattice and harmonic–linear–lattice ones. Also, corresponding analytical localized soliton solutions in terms of Mathieu and elliptic functions are studied, such as snake solitons, moving breathing solitons and oscillating solitons. Finally, some stable solitons are found by means of the stability analysis of the exact solutions with the split-step Fourier transform method. (author)