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A method for the study of steady-state nonlinear modes for Gross-Pitaevskiiequation (GPE) is described. It is based on exact statement about coding of thesteady-state solutions of GPE which vanish as $x\to+\infty$ by reals. Thisallows to fulfill {\it demonstrative computation} of nonlinear modes of GPEi.e. the computation which allows to guarantee that {\it all} nonlinear modeswithin a given range of parameters have been found. The method has been appliedto GPE with quadratic and double-well potential, for both, repulsive andattractive nonlinearities. The bifurcation diagrams of nonlinear modes in thesecases are represented. The stability of these modes has been discussed.Comment: 21 pages, 6 figure

Nonlinear modes for the Gross–Pitaevskii equation—a demonstrative computation approach