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Title: Three-dimensional rogue waves in nonstationary parabolic potentials

Abstract

Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schroedinger (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.

Authors:
 [1];  [2];  [3]
  1. Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100080 (China)
  2. Centro de Fisica Teorica e Computacional and Departamento de Fisica, Faculdade de Cienacias, Universidade de Lisboa, Lisboa 1649-003 (Portugal)
  3. Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies, Australian National University, Canberra, Australian Capital Territory 0200 (Australia)
Publication Date:
OSTI Identifier:
21464507
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)
Additional Journal Information:
Journal Volume: 82; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevE.82.036610; (c) 2010 The American Physical Society; Journal ID: ISSN 1539-3755
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; EXACT SOLUTIONS; INTEGRAL CALCULUS; NONLINEAR OPTICS; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; SCHROEDINGER EQUATION; SYMMETRY; THREE-DIMENSIONAL CALCULATIONS; TIME DEPENDENCE; TRANSFORMATIONS; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL SOLUTIONS; MATHEMATICS; OPTICS; PARTIAL DIFFERENTIAL EQUATIONS; WAVE EQUATIONS

Citation Formats

Zhenya, Yan, International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, Konotop, V V, and Akhmediev, N. Three-dimensional rogue waves in nonstationary parabolic potentials. United States: N. p., 2010. Web. doi:10.1103/PHYSREVE.82.036610.
Zhenya, Yan, International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, Konotop, V V, & Akhmediev, N. Three-dimensional rogue waves in nonstationary parabolic potentials. United States. https://doi.org/10.1103/PHYSREVE.82.036610
Zhenya, Yan, International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, Konotop, V V, and Akhmediev, N. 2010. "Three-dimensional rogue waves in nonstationary parabolic potentials". United States. https://doi.org/10.1103/PHYSREVE.82.036610.
@article{osti_21464507,
title = {Three-dimensional rogue waves in nonstationary parabolic potentials},
author = {Zhenya, Yan and International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016 and Konotop, V V and Akhmediev, N},
abstractNote = {Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schroedinger (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.},
doi = {10.1103/PHYSREVE.82.036610},
url = {https://www.osti.gov/biblio/21464507}, journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},
issn = {1539-3755},
number = 3,
volume = 82,
place = {United States},
year = {Wed Sep 15 00:00:00 EDT 2010},
month = {Wed Sep 15 00:00:00 EDT 2010}
}