Elliptical and rectangular solitons in media with competing cubic–quintic nonlinearities

We demonstrate two new types of non-circularly-symmetric solitons, the elliptical and rectangular solitons, which can be sustained by the cubic–quintic nonlinearity in the nonlinear Schrödinger equation with a linear potential well. The characteristics of these solitons are investigated in some detail. Notably, the elliptical and circular solitons can transform into each other, and similarly the rectangular and square solitons can transform into each other. Interestingly, we find that elliptical and rectangular solitons can also transform into each other—a phenomenon not readily seen among different types of solitons. In addition, the rotation of elliptical and rectangular solitons is displayed as well. Finally, we find that stable vortex modes of elliptical and rectangular solitons can be also supported by our model.