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Yan, Zhenya; Konotop, V. V.; Akhmediev, N. (2010)
Languages: English
Types: Article,Preprint
Subjects: Physics - Classical Physics, Mathematical Physics, Nonlinear Sciences - Pattern Formation and Solitons, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematics - Analysis of PDEs

Classified by OpenAIRE into

arxiv: Nonlinear Sciences::Pattern Formation and Solitons, Nonlinear Sciences::Exactly Solvable and Integrable Systems
Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation with variable coefficients and parabolic potential to the (1+1)-dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1)-dimensional case to the variety of solutions of integrable NLS equation of (1+1)-dimensional case. As an example, we illustrated our technique using two lowest order rational solutions of the NLS equation as seeding functions to obtain rogue wave-like solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wave-like solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and BECs.
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    • [1] G. W. Bluman and S. Kumei, Symmetries and differential equations (Springer-Verlag, New York, 1989); P. J. Olver, Application of Lie groups to differential equations (2nd Ed.) (Springer-Verlag, New York, 1993); G. W. Bluman, A. Cheviakov, and S. Anco, Applications of symmetry methods to partial differential equations (Springer, New York, 2009); G. W. Bluman and Z. Y. Yan, Euro. J. Appl. Math. 16, 239 (2005).
    • [2] M. Ablowitz and H. Segur, Solitons and the inverse scattering transform (SIAM, Philadelphia, 1981).
    • [3] R. Y. Chiao, E. Garmair and C. H. Townes, Phys. Rev. Lett., 13, 479 (1964).
    • [4] V. N. Vlasov, I. A. Petrishev and V. I. Talanov, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 14, 1353 (1971).
    • [5] L. Berge, Phys. Rep. 303, 259 (1998).
    • [6] C. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear optics: Electromagnetic waves in nonlinear dispersive media, (VINITI, Moscow, 1964).
    • [7] L. Gagnon, JOSA B 7, 1098 (1990).
    • [8] Y. S. Kivshar, G. P. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, New York, 2003). B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical OPt. 7, 53R (2005).
    • [9] L. Pitaevskii and S. Stringari, Bose-Einstein condensation (Oxford University Press, Oxford, 2003); R. Carretero-Gonz´alez, D. J. Frantzeskakis, and P. G. Kevrekidis, Nonlinearity 21, R139 (2008); F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999); A. J. Legge, Rev. Mod. Phys. 73, 307 (2001).
    • [10] Z. Y. Yan and V. V. Konotop, Phys. Rev. E 80, 036607 (2009).
    • [11] Z. Y. Yan and C. Hang, Phys. Rev. A 80, 063626 (2009).
    • [12] A. R. Osborne, Nonlinear ocean waves, (Academic Press, 2009).
    • [13] A. Montina, U. Bortolozzo, S. Residori, and F. T. Arecchi, Phys. Rev. Lett., 103, 173901 (2009)
    • [14] M. Shats, H. Punzmann, and H. Xia, Phys. Rev. Lett., 104, 104503 (2010).
    • [15] D. R. Solli, C. Ropers, P. Koonath and B. Jalali, Nature 450, 1054 (2007); D. R. Solli, C. Ropers, and B. Jalali, Phys. Rev. Lett. 101, 233902 (2008).
    • [16] D.-I. Yeom and B. Eggleton, Nature, 450, 953 (2007).
    • [17] Yu. V. Bludov, V. V. Konotop and N. Akhmebiev, Opt. Lett. 34, 3015 (2009).
    • [18] Z. Y. Yan, Phys. Lett. A 374, 672 (2010).
    • [19] Yu. V. Bludov, V. V. Konotop, and N. Akhmediev, Phys. Rev. A, 80, 033610 (2009).
    • [20] L. Stenflo and M. Marklund, J. Plasma Phys. 76, 293 (2010).
    • [21] Z. Y. Yan, e-print arXiv:0911.4259, 2009.
    • [22] J. Belmonte-Beitia, V. M. P´erez-Garc´ıa, V. Vekslerchik, and V. V. Konotop, Phys. Rev. Lett. 100, 164102 (2008).
    • [23] N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Lett. A 373, 2137 (2009).
    • [24] N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009). See also: N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, Sov. Phys. JETP 89, 1542 (1985).
    • [25] N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, Phys. Rev. E 80, 026601 (2009).
    • [26] A. Ankiewicz, P. A. Clarkson, and N. Akhmediev, J. Phys. A 43, 122002 (2010).
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