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Vortex Solitons for a Class of Schrödinger Equation with Square Root Nonlinear Term
College of Sciences, University of Shanghai for Science and Technology, Shanghai, China
- 1 College of Sciences, University of Shanghai for Science and Technology, Shanghai, China
Advances in Pure Mathematics·Volume 10 (2020)·Pages 174–180·Published 8 April 2020·DOI10.4236/apm.2020.104011
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Abstract
In this paper, we prove an existence theory for ring-profiled optical vortex solitons via constrained minimization, which are considered in the context of an electromagnetic light wave propagating in a nonlinear media and governed by a nonlinear Schrödinger type equation with square root nonlinear term.
KeywordsOptical Vortex SolitonsSquare Root NonliearConstrained Minimization
- Adhikari, S.K. (2010) Localization of a Bose-Einstein Condensate Vortex in a Bichromatic Optical Lattice. Physical Review A, 81, Article ID: 043636. https://doi.org/10.1103/PhysRevA.81.043636
- Davydova, T.A. and Yakimenko, A.I. (2004) Stable Multi-Charged Localized Optical Vortices in Cubicquintic Nonlinear Media. Journal of Optics A: Pure and Applied Optics, 97, S197-S201. https://doi.org/10.1088/1464-4258/6/5/010
- Kartashov, Y.V., Vysloukh, V.A. and Torner, L. (2004) Rotary Solitons in Bessel Optical Lattices. Physical Review Letters, 93, Article ID: 093904. https://doi.org/10.1103/PhysRevLett.93.093904
- Kartashov, Y.V., Vysloukh, V.A. and Torner, L. (2005) Stable Ring Vortex Soltions in Bessel Optical Lattices. Physical Review Letters, 94, Article ID: 043902. https://doi.org/10.1103/PhysRevLett.94.043902
- Mamaev, A.V., Saffman, M. and Zozulya, A.A. (1996) Propagation of Stripe Beams in Nonlinear Media: Snake Instability and Creation of Optical Vortices. Physical Review Letters, 76, 2262-2265. https://doi.org/10.1103/PhysRevLett.76.2262
- Neshev, D., Alexander, T.J., Ostrovskaya, E.A., Kivshar, Y.S., Martin, H., Makasyuk, I. and Chen, Z. (2004) Observation of Discrete Vortex Solitons in Optically-Induced Photonic Lattices. Physical Review Letters, 92, Article ID: 123903. https://doi.org/10.1103/PhysRevLett.92.123903
- Rozas, D., Law, C.T. and Swartzlander Jr., G.A. (1997) Propagation Dynamics of Optical Vortices. Journal of the Optical Society of America B, 14, 3054-3065. https://doi.org/10.1364/JOSAB.14.003054
- Skryabin, D.V. and Firth, W.J. (1998) Dynamics of Self-Trapped Beams with Phase Dislocation in Saturable Kerr and Quadratic Nonlinear Media. Physical Review E, 58, 3916-3930. https://doi.org/10.1103/PhysRevE.58.3916
- Lin, T.C., Belić, M.R., Petrović, M.S., Hajaiej, H. and Chen, G. (2017) The Virial Theorem and Ground State Energy Estimates of Nonlinear Schrödinger Equations in with Square Root and Saturable Nonlinearities in Nonlinear Optics. Calculus of Variations and Partial Differential Equations, 56, Article No. 147. https://doi.org/10.1007/s00526-017-1251-4
- Liu, C. and Ren, Q. (2015) On the Steady-State Solutions of a Nonlinear Photonic Lattice Model. Journal of Mathematical Physics, 53, Article ID: 031501. https://doi.org/10.1063/1.4914333
- Petroskia, M.M., Petrovica, M.S. and Belica, M.R. (2007) Quasi-Stable Propagation of Vortices and Soliton Clusters in Previous Saturable Kerr Media with Square-Root Nonlinearity. Optics Communications, 279, Article ID: 196202. https://doi.org/10.1016/j.optcom.2007.07.006