Three-dimensional rogue waves in nonstationary parabolic potentials

Zhenya Yan*, V. V. Konotop, N. Akhmediev

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    147 Citations (Scopus)


    Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1) -dimensional inhomogeneous nonlinear Schrödinger (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 the (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 wavelike 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 wavelike solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and Bose-Einstein condensates.

    Original languageEnglish
    Article number036610
    JournalPhysical Review E
    Issue number3
    Publication statusPublished - 30 Sept 2010


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