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Keywords = nonlinear schrödinger equation with random potentials

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10 pages, 869 KB  
Article
Generation and Controllability of High-Dimensional Rogue Waves in an Electromagnetically Induced Transparent Medium
by Zhongyin Li, Ji Lin and Huijun Li
Mathematics 2023, 11(8), 1829; https://doi.org/10.3390/math11081829 - 12 Apr 2023
Viewed by 1550
Abstract
We propose a scheme to generate and control high-dimensional rogue waves in a coherent three-level Λ-type atomic system via electromagnetically induced transparency (EIT). Under EIT conditions, the probe field envelopes obey the non-integrable nonlinear Schrödinger equations (NLSE) with or without the external [...] Read more.
We propose a scheme to generate and control high-dimensional rogue waves in a coherent three-level Λ-type atomic system via electromagnetically induced transparency (EIT). Under EIT conditions, the probe field envelopes obey the non-integrable nonlinear Schrödinger equations (NLSE) with or without the external potential, which result from the stark (Zeeman) effect contributed by an electric (magnetic) field. By adjusting the amplitude and width of the initial pulse, we can generate the high-dimensional rogue waves and obtain the phase-transition curves of high-dimensional rogue waves. In the system, the far-detuned electric field, the random weak magnetic field, and the Gauss weak magnetic field are not conducive to the excitation of high-dimensional rogue waves. The results not only provide a theoretical basis for the experimental realization or prevention of the high-dimensional rogue waves, but also prove the possibility of generating and controlling the rogue waves in other high-dimensional non-integrable systems. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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12 pages, 251 KB  
Article
On the Wave Turbulence Theory for the Nonlinear Schrödinger Equation with Random Potentials
by Sergey Nazarenko, Avy Soffer and Minh-Binh Tran
Entropy 2019, 21(9), 823; https://doi.org/10.3390/e21090823 - 23 Aug 2019
Cited by 16 | Viewed by 3577
Abstract
We derive new kinetic and a porous medium equations from the nonlinear Schrödinger equation with random potentials. The kinetic equation has a very similar form compared to the four-wave turbulence kinetic equation in the wave turbulence theory. Moreover, we construct a class of [...] Read more.
We derive new kinetic and a porous medium equations from the nonlinear Schrödinger equation with random potentials. The kinetic equation has a very similar form compared to the four-wave turbulence kinetic equation in the wave turbulence theory. Moreover, we construct a class of self-similar solutions for the porous medium equation. These solutions spread with time, and this fact answers the “weak turbulence” question for the nonlinear Schrödinger equation with random potentials. We also derive Ohm’s law for the porous medium equation. Full article
(This article belongs to the Special Issue Statistical Mechanics and Mathematical Physics)
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