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:
-
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100080 (China)
- Centro de Fisica Teorica e Computacional and Departamento de Fisica, Faculdade de Cienacias, Universidade de Lisboa, Lisboa 1649-003 (Portugal)
- 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}
}