Gap solitons in elongated geometries: The one-dimensional Gross-Pitaevskii equation and beyond

  title={Gap solitons in elongated geometries: The one-dimensional Gross-Pitaevskii equation and beyond},
  author={Antonio Munoz Mateo and V. Delgado and Boris A. Malomed},
  journal={Physical Review A},
We report results of a systematic analysis of matter-wave gap solitons (GSs) in three-dimensional self-repulsive Bose-Einstein condensates (BECs) loaded into a combination of a cigar-shaped trap and axial optical-lattice (OL) potential. Basic cases of the strong, intermediate, and weak radial (transverse) confinement are considered, as well as settings with shallow and deep OL potentials. Only in the case of the shallow lattice combined with tight radial confinement, which actually has little… 
9 Citations
Accurate one-dimensional effective description of realistic matter-wave gap solitons
We consider stationary matter-wave gap solitons realized in Bose–Einstein condensates loaded in one-dimensional (1D) optical lattices and investigate whether the effective 1D equation proposed in
Quasi-one-dimensional Bose–Einstein condensates in nonlinear lattices
We consider the three-dimensional (3D) mean-field model for the Bose–Einstein condensate, with a one-dimensional (1D) nonlinear lattice (NL), which periodically changes the sign of the nonlinearity
Quasi-one-dimensional approximation for Bose–Einstein condensates transversely trapped by a funnel potential
Starting from the standard three-dimensional (3D) Gross–Pitaevskii equation (GPE) and using a variational approximation, we derive an effective one-dimensional nonpolynomial Schrödinger equation
Stable symmetry-protected 3D embedded solitons in Bose–Einstein condensates
The analysis of the Bogoliubov excitation spectrum as well as the long-term evolution after random perturbations proves the robustness of these nonlinear structures against any weak perturbation.
Nonlinear waves of Bose-Einstein condensates in rotating ring-lattice potentials
We analyze the dynamics of Bose-Einstein condensates loaded in rotating ring lattices made of a few sites, and show how rotation maps the states found in this finite system into those belonging to a
Effective Equations for Repulsive Quasi‐One Dimensional Bose–Einstein Condensates Trapped with Anharmonic Transverse Potentials
One‐dimensional nonlinear Schrödinger equations are derived to describe the axial effective dynamics of cigar‐shaped atomic repulsive Bose‐Einstein condensates trapped with anharmonic transverse
Soliton appearing in boson-fermion mixture at the third order of the interaction radius
In this paper we consider an ultra-cold mixture of boson and fermion atoms on the basis of quantum hydrodynamics. Small one-dimensional perturbations in such systems are being analyzed. A possibility
Exactly solvable Gross–Pitaevskii type equations
We suggest a method to construct exactly solvable Gross–Pitaevskii type equations, especially the variable-coefficient high-order Gross–Pitaevskii type equations. We show that there exists a relation


  • Rev. A 81, 063604
  • 2010
  • Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401
  • 2004
  • Rev. A 83, 021605
  • 2011
  • Rev. Lett. 89, 110401
  • 2002
  • Rev. A 67, 013602
  • 2003
An independent derivation of this formula was reported by F . Gerbier
  • Europhys . Lett .
  • 2004
  • Rev. Lett. 97, 110406
  • 2006
  • Rev. A 65, 043614 (2002); L. Salasnich, Laser Phys. 12, 198
  • 2002
Nuovo Cimento 20
  • 454 (1961); J. Math. Phys. 4, 195 (1963); L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451
  • 1961
  • Phys. Lett. B 18, 627
  • 2004