2017/05/26 by Qutaibeh Katatbeh, Katatbeh, Qutaibeh D., Dimitris M. Christodoulou +1 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Nonlinear Photonic Systems #Mechanical and Optical Resonators
paper · pdf · doi:10.48550/arxiv.1705.09721
We have previously formulated a simple criterion for deducing the intervals\nof oscillations in the solutions of second-order linear homogeneous\ndifferential equations. In this work, we extend analytically the same criterion\nto the cubic nonlinear Schr "odinger equations that describe Bose-Einstein\ncondensates. With this criterion guiding the search for solutions, we classify\nall types of solutions and we find new stationary solutions in the\nfree-particle cases that were not noticed previously because of limited\ncoverage in the adopted boundary conditions. The new solutions are produced by\nthe nonlinear terms of the differential equations and they continue to exist\nwhen various external potentials are also incorporated. Surprisingly, these\nsolutions appear when the nonlinearities are small.\n