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Three-dimensional rogue waves in nonstationary parabolic potentials Zhenya Yan,1,2,* V. V. Konotop,3
 

Summary: Three-dimensional rogue waves in nonstationary parabolic potentials
Zhenya Yan,1,2,* V. V. Konotop,3
and N. Akhmediev4
1
Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences,
Beijing 100080, China
2
International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, China
3
Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciênacias, Universidade de Lisboa,
Lisboa 1649-003, Portugal
4
Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies,
The Australian National University, Canberra, Australian Capital Territory 0200, Australia
Received 1 August 2010; published 30 September 2010
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 tech-

  

Source: Akhmediev, Nail - Research School of Physical Sciences and Engineering, Australian National University
Australian National University, Research School of Physical Sciences and Engineering, Optical Sciences Group

 

Collections: Engineering; Physics