Abstract
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.
Original language | English |
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Pages (from-to) | 10066-10077 |
Number of pages | 12 |
Journal | Optics Express |
Volume | 24 |
Issue number | 9 |
DOIs | |
Publication status | Published - 2 May 2016 |
Externally published | Yes |