Solitons in the discrete nonpolynomial Schrodinger equation
Апстракт
We introduce a species of the discrete nonlinear Schrodinger (DNLS) equation, which is a model for a self-attractive Bose-Einstein condensate confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction. The equation is derived as a discretization of the respective nonlinear nonpolynomial Schrodinger equation. Unlike previously considered varieties of one-dimensional DNLS equations, the present discrete model admits on-site collapse. We find two families of unstaggered on-site-centered discrete solitons, stable and unstable ones, which include, respectively, broad and narrow solitons, their stability exactly complying with the Vakhitov-Kolokolov criterion. Unstable on-site solitons either decay or transform themselves into robust breathers. Intersite-centered unstaggered solitons are unstable to collapse; however, they may be stabilized by the application of a sufficiently strong kick, which turns them into moving localized modes. Persistently... moving solitons can be readily created too by the application of the kick to stable on-site unstaggered solitons. In the same model, staggered solitons, which are counterparts of gap solitons in the continuum medium, are possible if the intrinsic nonlinearity is self-repulsive. All on-site staggered solitons are stable, while intersite ones have a small instability region. The staggered solitons are immobile.
Извор:
Physical Review A, 2008, 78, 1
DOI: 10.1103/PhysRevA.78.013616
ISSN: 1050-2947
WoS: 000258180300172
Scopus: 2-s2.0-47749126617
Колекције
Институција/група
VinčaTY - JOUR AU - Maluckov, Aleksandra AU - Hadžievski, Ljupčo AU - Malomed, Boris A. AU - Salasnich, Luca PY - 2008 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3502 AB - We introduce a species of the discrete nonlinear Schrodinger (DNLS) equation, which is a model for a self-attractive Bose-Einstein condensate confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction. The equation is derived as a discretization of the respective nonlinear nonpolynomial Schrodinger equation. Unlike previously considered varieties of one-dimensional DNLS equations, the present discrete model admits on-site collapse. We find two families of unstaggered on-site-centered discrete solitons, stable and unstable ones, which include, respectively, broad and narrow solitons, their stability exactly complying with the Vakhitov-Kolokolov criterion. Unstable on-site solitons either decay or transform themselves into robust breathers. Intersite-centered unstaggered solitons are unstable to collapse; however, they may be stabilized by the application of a sufficiently strong kick, which turns them into moving localized modes. Persistently moving solitons can be readily created too by the application of the kick to stable on-site unstaggered solitons. In the same model, staggered solitons, which are counterparts of gap solitons in the continuum medium, are possible if the intrinsic nonlinearity is self-repulsive. All on-site staggered solitons are stable, while intersite ones have a small instability region. The staggered solitons are immobile. T2 - Physical Review A T1 - Solitons in the discrete nonpolynomial Schrodinger equation VL - 78 IS - 1 DO - 10.1103/PhysRevA.78.013616 ER -
@article{ author = "Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A. and Salasnich, Luca", year = "2008", abstract = "We introduce a species of the discrete nonlinear Schrodinger (DNLS) equation, which is a model for a self-attractive Bose-Einstein condensate confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction. The equation is derived as a discretization of the respective nonlinear nonpolynomial Schrodinger equation. Unlike previously considered varieties of one-dimensional DNLS equations, the present discrete model admits on-site collapse. We find two families of unstaggered on-site-centered discrete solitons, stable and unstable ones, which include, respectively, broad and narrow solitons, their stability exactly complying with the Vakhitov-Kolokolov criterion. Unstable on-site solitons either decay or transform themselves into robust breathers. Intersite-centered unstaggered solitons are unstable to collapse; however, they may be stabilized by the application of a sufficiently strong kick, which turns them into moving localized modes. Persistently moving solitons can be readily created too by the application of the kick to stable on-site unstaggered solitons. In the same model, staggered solitons, which are counterparts of gap solitons in the continuum medium, are possible if the intrinsic nonlinearity is self-repulsive. All on-site staggered solitons are stable, while intersite ones have a small instability region. The staggered solitons are immobile.", journal = "Physical Review A", title = "Solitons in the discrete nonpolynomial Schrodinger equation", volume = "78", number = "1", doi = "10.1103/PhysRevA.78.013616" }
Maluckov, A., Hadžievski, L., Malomed, B. A.,& Salasnich, L.. (2008). Solitons in the discrete nonpolynomial Schrodinger equation. in Physical Review A, 78(1). https://doi.org/10.1103/PhysRevA.78.013616
Maluckov A, Hadžievski L, Malomed BA, Salasnich L. Solitons in the discrete nonpolynomial Schrodinger equation. in Physical Review A. 2008;78(1). doi:10.1103/PhysRevA.78.013616 .
Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., Salasnich, Luca, "Solitons in the discrete nonpolynomial Schrodinger equation" in Physical Review A, 78, no. 1 (2008), https://doi.org/10.1103/PhysRevA.78.013616 . .