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.

中文翻译：

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具有竞争三次五次非线性的介质中的椭圆形和矩形孤子


我们证明了两种新型非圆对称孤子，即椭圆孤子和矩形孤子，它们可以通过具有线性势阱的非线性薛定谔方程中的三次-五次非线性来维持。对这些孤子的特性进行了一些详细的研究。值得注意的是，椭圆形和圆形孤子可以相互转化，类似地矩形和方形孤子也可以相互转化。有趣的是，我们发现椭圆形和矩形孤子也可以相互转化——这种现象在不同类型的孤子中并不容易看到。此外，还显示了椭圆形和矩形孤子的旋转。最后，我们发现我们的模型也可以支持椭圆形和矩形孤子的稳定涡旋模式。