Pseudo-Arclength Continuation Algorithms for Binary Rydberg-Dressed Bose-Einstein Condensates (Communications in Computational Physics, 2018)
We study pseudo-arclength continuation methods for both Rydberg-dressedBose-Einstein condensates (BEC), and binary Rydberg-dressed BEC which are governedby the Gross-Pitaevskii equations (GPEs). A divide-and-conquer technique isproposed for rescaling the range/ranges of nonlocal nonlinear term/terms, whichgives enough information for choosing a proper stepsize. This guarantees that the solutioncurve we wish to trace can be precisely approximated. In addition, the groundstate solution would successfully evolve from one peak to vortices when the affect ofthe rotating term is imposed. Moreover, parameter variables with different number ofcomponents are exploited in curve-tracing. The proposed methods have the advantageof tracing the ground state solution curve once to compute the contours for various valuesof the coefficients of the nonlocal nonlinear term/terms. Our numerical results areconsistent with those published in the literatures.