Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach

Details Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach

2007-03-05

arxiv.org/abs/nlin/0703006v1

Nonlinear Sciences

Pattern Formation and Solitons

21 pages, 6 figures

Scientific paper

10.1088/0951-7715/20/9/004

A method for the study of steady-state nonlinear modes for Gross-Pitaevskii equation (GPE) is described. It is based on exact statement about coding of the steady-state solutions of GPE which vanish as $x\to+\infty$ by reals. This allows to fulfill {\it demonstrative computation} of nonlinear modes of GPE i.e. the computation which allows to guarantee that {\it all} nonlinear modes within a given range of parameters have been found. The method has been applied to GPE with quadratic and double-well potential, for both, repulsive and attractive nonlinearities. The bifurcation diagrams of nonlinear modes in these cases are represented. The stability of these modes has been discussed.

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