248 citations · 2.6k across the 72 of their papers we have counts for
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Propagation dynamics of abruptly autofocusing circular Airy-Gaussian vortex beams in the fractional Schrödinger equation
Shangling He, Boris A. Malomed, Dumitru Mihalache +4
We introduce axisymmetric Airy-Gaussian vortex beams in a model of an optical system based on the (2+1)-dimensional fractional Schrödinger equation, characterized by its Lévy index…
Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities
Pengfei Li, Boris A. Malomed, Dumitru Mihalache
We demonstrate that fractional cubic-quintic nonlinear Schrödinger equation,characterized by its Lévy index, maintains ring-shaped soliton clusters ("necklaces") carrying orbital a…
Stabilization of single- and multi-peak solitons in the fractional nonlinear Schroedinger equation with a trapping potential
Yunli Qiu, Boris A. Malomed, Dumitru Mihalache +3
We address the existence and stability of localized modes in the framework of the fractional nonlinear Schroedinger equation (FNSE) with the focusing cubic or focusing-defocusing c…
Reductions of the (4 + 1)-dimensional Fokas equation and their solutions
Yulei Cao, Jingsong He, Yi Cheng +1
An integrable extension of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations is investigated in this paper.We will refer to this integrable extension as the (4+1)…
Symmetry breaking of spatial Kerr solitons in fractional dimension
Pengfei Li, Boris A. Malomed, Dumitru Mihalache
We study symmetry breaking of solitons in the framework of a nonlinear fractional Schrödinger equation (NLFSE), characterized by its Lévy index, with cubic nonlinearity and a symme…
Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity
Pengfei Li, Boris A. Malomed, Dumitru Mihalache
We address the existence and stability of vortex-soliton (VS) solutions of the fractional nonlinear Schrödinger equation (NLSE) with competing cubic-quintic nonlinearities and the…