Three-dimensional rogue waves in nonstationary parabolic potentials

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.82.036610· OSTI ID:21464507

Zhenya, Yan ^[1]; Konotop, V V ^[2]; Akhmediev, N ^[3]

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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)

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.

• OSTI ID: 21464507
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevE.82.036610; (c) 2010 The American Physical Society; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

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