Three-dimensional rogue waves in non-stationary parabolic potentials

Article, Preprint English OPEN
Yan, Zhenya ; Konotop, V. V. ; Akhmediev, N. (2010)
  • Publisher: AMER PHYSICAL SOC
  • Journal: PHYSICAL REVIEW E (issn: 1539-3755)
  • Related identifiers: doi: 10.1103/PhysRevE.82.036610
  • Subject: Physics - Classical Physics | Mathematical Physics | Nonlinear Sciences - Pattern Formation and Solitons | Nonlinear Sciences - Exactly Solvable and Integrable Systems | Mathematics - Analysis of PDEs
    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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