Dynamics of nonlinear waves in two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and potentials Academic Article uri icon


  • We derive analytical solutions to the cubic-quintic nonlinear Schrödinger equation with potentials and nonlinearities depending on both propagation distance and transverse space. Among other, circle solitons and multi-peaked vortex solitons are found. These solitary waves propagate self-similarly and are characterized by three parameters, the modal numbers m and n, and the modulation depth of intensity. We find that the stable fundamental solitons with m = 0 and the low-order solitons with m = 1, n ≤ 2 can be supported with the energy eigenvalues E = 0 and E ≠ 0. However, higher-order solitons display unstable propagation over prolonged distances. The stability of solutions is examined by numerical simulations.

author list (cited authors)

  • Xu, S., Cheng, J., Belić, M. R., Hu, Z., & Zhao, Y.

citation count

  • 14

publication date

  • April 2016