## Abstract

We consider a class of nonlinear Schrödinger/Gross-Pitaeveskii (NLS-GP) equations, i.e., NLS with a linear potential. NLS-GP plays an important role in the mathematical modeling of nonlinear optical as well as macroscopic quantum phenomena (BEC). We obtain conditions for a symmetry-breaking bifurcation in a symmetric family of states as M, the squared L ^{2} norm (particle number, optical power), is increased. The bifurcating asymmetric state is a "mixed mode" which, near the bifurcation point, is approximately a superposition of symmetric and antisymmetric modes. In the special case where the linear potential is a double well with well-separation L, we estimate N _{cr}(L), the symmetry breaking threshold. Along the "lowest energy" symmetric branch, there is an exchange of stability from the symmetric to the asymmetric branch as N is increased beyond N _{cr}.

Original language | English (US) |
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Pages (from-to) | 566-604 |

Number of pages | 39 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 40 |

Issue number | 2 |

DOIs | |

State | Published - 2008 |

## Keywords

- Bound state
- Gross-Pitaevskii
- Nonlinear schrodinger
- Soliton

## ASJC Scopus subject areas

- Analysis
- Computational Mathematics
- Applied Mathematics