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3042798170
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For a list of reviews on solitons in physics and mathematics
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For a list of reviews on solitons in physics and mathematics see A. Degasperis, Am. J. Phys. 66, 486 (1998).
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(1998)
Am. J. Phys.
, vol.66
, pp. 486
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Degasperis, A.1
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3
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85036250005
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E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge University Press, Cambridge, UK, 1990), Chap. 5 (in particular p. 127)
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E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge University Press, Cambridge, UK, 1990), Chap. 5 (in particular p. 127).
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6
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85076161456
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Just before this current paper was submitted, we were informed by Professor Alain Barthelemy that his group had in fact observed self-trapped necklaces in Kerr media back in 1993, yet they had trouble publishing it. Therefore, it has appeared in conference proceedings only At the time Ref. 5 was published, we had no idea about Barthelemy’s experiments
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Just before this current paper was submitted, we were informed by Professor Alain Barthelemy that his group had in fact observed self-trapped necklaces in Kerr media back in 1993, yet they had trouble publishing it. Therefore, it has appeared in conference proceedings only. See A. Barthelemy, C. Froehly, and M. Shalaby, SPIE International Symposium on Optics, Quebec, 1993 [J. Soc. Photo-Opt. Instrum. Eng. 2041, 104 (1993)]. At the time Ref. 5 was published, we had no idea about Barthelemy’s experiments.
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(1993)
J. Soc. Photo-Opt. Instrum. Eng.
, vol.2041
, pp. 104
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Barthelemy, A.1
Froehly, C.2
Shalaby, M.3
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7
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85036301781
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A recent observation of necklace-ring solitonlike patterns was made in a two-dimensional array of vertical cavity surface emitting lasers, and reported by J. Scheuer, D. Arbel, and M. Orenstein, Nonlinear Guided Waves and Their Applications Conference (Optical Society of America, Washington, DC, 1999), pp. 180–182. The nonlinear medium involved is NOT a Kerr medium, but rather a (resonant) laser medium, so the underlying equation is the complex Ginzburg-Landau equation and not the cubic NLSE as in 5 and in the present work. Nonetheless, the observed necklace-ring solitons in both cases seem to have many features in common
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A recent observation of necklace-ring solitonlike patterns was made in a two-dimensional array of vertical cavity surface emitting lasers, and reported by J. Scheuer, D. Arbel, and M. Orenstein, Nonlinear Guided Waves and Their Applications Conference (Optical Society of America, Washington, DC, 1999), pp. 180–182. The nonlinear medium involved is NOT a Kerr medium, but rather a (resonant) laser medium, so the underlying equation is the complex Ginzburg-Landau equation and not the cubic NLSE as in 5 and in the present work. Nonetheless, the observed necklace-ring solitons in both cases seem to have many features in common.
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0026116887
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Azimuthal modulation instability of uniform bright ring beams (carrying zero topological charge) in self-focusing Kerr media was demonstrated theoretically by
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Azimuthal modulation instability of uniform bright ring beams (carrying zero topological charge) in self-focusing Kerr media was demonstrated theoretically by Y. Chen and A. W. Snyder, Europhys. Lett. 27, 565 (1992)
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(1992)
Europhys. Lett.
, vol.27
, pp. 565
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Chen, Y.1
Snyder, A.W.2
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0028428751
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4 in Ref. 5. To our knowledge, this instability has not yet been observed experimentally in Kerr media. Uniform bright ring beams with zero topological charge are azimuthally unstable also in saturable self-focusing media as shown theoretically by
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See also Fig. 4 in Ref. 5. To our knowledge, this instability has not yet been observed experimentally in Kerr media. Uniform bright ring beams with zero topological charge are azimuthally unstable also in saturable self-focusing media as shown theoretically by J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, R3170 (1994).
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(1994)
Phys. Rev. A
, vol.49
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Atai, J.1
Chen, Y.2
Soto-Crespo, J.M.3
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14
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77951937567
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Azimuthal modulation instability of bright ring beams that carry nonzero topological charge, in self-focusing (Kerr and non-Kerr) media was demonstrated theoretically by several groups, including
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Azimuthal modulation instability of bright ring beams that carry nonzero topological charge, in self-focusing (Kerr and non-Kerr) media was demonstrated theoretically by several groups, including V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, J. Mod. Opt. 39, 2277 (1992)
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(1992)
J. Mod. Opt.
, vol.39
, pp. 2277
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Kruglov, V.I.1
Logvin, Y.A.2
Volkov, V.M.3
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The vortex-ring beam disintegrates into multiple isolated filaments. In Kerr media, the isolated filaments are of course unstable. In saturable self-focusing media, the filaments are stable and can interact with one another (if they are close enough to each other) or simply move outwards like free particles. Experimentally, disintegration of vortex-ring beams in saturable self-focusing media was observed by
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The vortex-ring beam disintegrates into multiple isolated filaments. In Kerr media, the isolated filaments are of course unstable. In saturable self-focusing media, the filaments are stable and can interact with one another (if they are close enough to each other) or simply move outwards like free particles. Experimentally, disintegration of vortex-ring beams in saturable self-focusing media was observed by V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996)
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(1996)
Phys. Rev. Lett.
, vol.76
, pp. 2698
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Tikhonenko, V.1
Christou, J.2
Luther-Davies, B.3
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atomic vapor and by in photorefractives. To our knowledge, the disintegration of vortex-ring beams in self-focusing Kerr media was not observed experimentally yet
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in atomic vapor and by Z. Chen, M. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, Opt. Lett. 22, 1751 (1997) in photorefractives. To our knowledge, the disintegration of vortex-ring beams in self-focusing Kerr media was not observed experimentally yet.
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(1997)
Opt. Lett.
, vol.22
, pp. 1751
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Chen, Z.1
Shih, M.2
Segev, M.3
Wilson, D.W.4
Muller, R.E.5
Maker, P.D.6
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J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. Smith, Opt. Lett. 15, 471 (1990).
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(1990)
Opt. Lett.
, vol.15
, pp. 471
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Aitchison, J.S.1
Weiner, A.M.2
Silberberg, Y.3
Oliver, M.K.4
Jackel, J.L.5
Leaird, D.E.6
Vogel, E.M.7
Smith, P.W.8
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L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Mediua, 2nd ed. (Butterworth-Heinenann, Oxford, 1982), Chap. XIII, p. 382
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L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Mediua, 2nd ed. (Butterworth-Heinenann, Oxford, 1982), Chap. XIII, p. 382.
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Interestingly, in our simulations, we never find a nonexpanding necklace that remains stable forever, we were able to adjust and optimize the necklace parameters so that it is nonexpanding and remains stable for a longer distance, but such fine tuning is most probably beyond experimental relevance. What we show in Fig. 77 is an example where the fine tuning is within reasonable experimental reach
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Interestingly, in our simulations, we never find a nonexpanding necklace that remains stable forever, we were able to adjust and optimize the necklace parameters so that it is nonexpanding and remains stable for a longer distance, but such fine tuning is most probably beyond experimental relevance. What we show in Fig. 77 is an example where the fine tuning is within reasonable experimental reach.
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