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Three-dimensional rogue waves in nonstationary parabolic potentials.
MedLine Citation:
PMID:  21230206     Owner:  NLM     Status:  In-Process    
Abstract/OtherAbstract:
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.
Authors:
Zhenya Yan; V V Konotop; N Akhmediev
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Publication Detail:
Type:  Journal Article     Date:  2010-09-30
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  82     ISSN:  1550-2376     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2010 Sep 
Date Detail:
Created Date:  2011-01-14     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  036610     Citation Subset:  -    
Affiliation:
Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100080, China. zyyan_math@yahoo.com
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