Splitting the NLS breather by an emerging localized potential

  Oleksandr Marchukov [1]  ,  Boris Malomed [1]  ,  Vladimir Yurovsky [2]  ,  Maxim Olshanii [3]  ,  Vanja Dunjko [3]  ,  Randall Hulet [4]  
[1] Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University
[2] School of Chemistry, Faculty of Engineering, Tel Aviv University
[3] Department of Physics, University of Massachusetts Boston, Boston, USA
[4] Department of Physics and Astronomy, Rice University, Houston, Texas, USA



We consider a one-dimensional interacting Bose gas described by the Gross-Pitaevskii equation (GPE) with an attractive cubic nonlinearity.  

In addition to well-known bright solitons, such equation also has higher-order solutions, in particular 2-solitons, alias breathers. We consider the evolution

of the breather interacting with a suddenly emerging narrow potential barrier, which is a situation with direct applications to nonlinear optics and BEC.

Depending on the barrier's height and initial position of the center of the breather, it may either split into constituent solitons or start moving as a whole. By means

of systematic simulations, we explore outcomes of the interaction in the parameter space of the model with both attractive and repulsive linear barriers, as well

as with repulsive nonlinear ones. We show that the ratio of the amplitudes of the emerging free solitons may be different from the expected 3:1 relation, exhibiting,

 in general, rather complex patterns. We identify the limit position of the breather that separates the splitting regime and unidirectional motion, and compare it with

an analytical estimate, that provides a close value.