Envelope periodic and solitary solutions to one dimensional Gross-Pitaevskii equation in Bose-Einstein condensates. (Chinese. English summary) Zbl 1212.35447
Summary: The construction of exact solutions of nonlinear Schrödinger equations plays an important role in understanding the dynamic evolution of Bose-Einstein condensates. The Jacobi elliptic function expansion method is applied to construct the envelope periodic solutions to one dimensional Gross-Pitaevskii equation in Bose-Einstein condensates. The envelope periodic solutions can degenerate to the envelope solitary solutions under the limited condition.
MSC:
35Q55 | NLS equations (nonlinear Schrödinger equations) |
35Q51 | Soliton equations |
82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |