## Abstract

We calculate the Lax pairs of homogeneous and inhomogeneous one-dimensional time-dependent Gross-Pitaevskii equations with time-dependent scattering length. The inhomogeneity corresponds to linear and quadratic potentials. Our approach introduces a systematic method of searching for the Lax pair corresponding to a given differential equation. We derive known Lax pairs for the Gross-Pitaevskii equation with homogeneous and quadratic potentials and time-dependent scattering length. We also derive new Lax pairs corresponding to a Gross-Pitaevskii equation with a linear potential. Using the resulting Lax pairs, the Darboux transformation can be performed and exact solutions of the Gross-Pitaevskii equation can be obtained for experimentally relevant cases such as solitonic solutions.

Original language | English |
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Article number | 002 |

Pages (from-to) | 9679-9691 |

Number of pages | 13 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 |

Issue number | 31 |

DOIs | |

Publication status | Published - Aug 4 2006 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy