Akhmediev, N.

Bandelow, U.

English

Электронная библиотека БГУ

 23
Linear and nonlinear guided modes in a parabolic potential 
V.V. Konotop, D.A. Zezyulin 
University of Lisbon, Lisbon, Portugal, e-mail: konotop@cii.fc.ul.pt 
 
We describe the families of nonlinear modes of the nonlinear Schrodinger 
equation with the PT-symmetric harmonic potential. The found modes display a 
number of interesting features. In particular, even when they bifurcate from the 
different eigenstates of the underlying linear problem, they can belong to the 
same family of nonlinear modes. We also show that by proper adjustment of the 
gain/loss gradient it is possible to enhance stability of small-amplitude and 
strongly nonlinear modes comparing to the well-studied case of the real harmonic 
potential. Implications of the above properties for the guidance of optical beams, 
in particular for giant amplification of the guided modes will also be discussed. 
A part of this work is done in collaboration with V. S. Shchesnovich. 
 
Dynamics of Lang-Kobayshi laser equations with large control coefficient 
E.V. Grigorieva, I.S. Kaschenko, S.A. Kaschenko 
Higher Mathematics Department, Belarus State Economical University, Minsk, 
Belarus, e-mail: grigorieva@tut.by 
 
We study dynamics of single-mode semiconductor laser under strong external 
optical feedback. The model introduced by Lang and Kobayashi includes terms 
with delayed argument. In the case of large control coefficient we derive 
continual sets of quasi-normal forms in local vicinity of the bifurcation 
parameters. On the base of such parabolic equations we discuss the phenomenon 
of multistable cycles and tori in the delayed system. 
 
Rogue waves in the Sasa-Satsuma equation 
U. Bandelow, N. Akhmediev 
WIAS Berlin, Germany, e-mail: bandelow@wias-berlin.de 
 
We investigate solutions of the Sasa-Satsuma equation (SSE), which is an 
integrable extension of the nonlinear Schrodinger equation (NLSE). In particular 
we demonstrate the lowest order rogue wave solutions for several parameters. In 
contrast to the Peregrine solution of the NLSE, these rogue wave solutions are 
significantly more involved and contain polynomials of fourth order rather than 
of second order in the corresponding expressions. When the extension parameter 
of the SSE is reduced to zero we obtain the correct limiting case of Peregrine 
solution of the NLSE.  
Literature: U. Bandelow and N. Akhmediev, “Persistence of rogue waves in extended 
nonlinear Schrodinger equations: integrable Sasa-Satsuma case”, Phys. Lett. A, 376, 
1558-1561 (2012) 


Rogue waves in the Sasa-Satsuma equation

http://elib.bsu.by/bitstream/123456789/24867/1/FANS_2012_23.pdf

Rogue waves in the Sasa-Satsuma equation

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