Discrete localized modes supported by an inhomogeneous defocusing nonlinearity
Апстракт
We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF) onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete bright solitons, which do not exist in lattices with the spatially uniform SDF nonlinearity. The UnST solitons coexist with stable staggered (ST) localized modes, which are always possible under the defocusing onsite nonlinearity. The results are obtained in a numerical form and also by means of variational approximation (VA). In the semi-infinite (truncated) system, some solutions for the UnST surface solitons are produced in an exact form. On the contrary to surface discrete solitons in uniform truncated lattices, the threshold value of the norm vanishes for the UnST solitons in the present system. Stability regions for the novel UnST solitons are identified. The same results imply the existence of ST discrete solitons in lattices with the spatially gr...owing self-focusing nonlinearity, where such solitons cannot exist either if the nonlinearity is homogeneous. In addition, a lattice with the uniform onsite SDF nonlinearity and exponentially decaying intersite coupling is introduced and briefly considered. Via a similar mechanism, it may also support UnST discrete solitons. The results may be realized in arrayed optical waveguides and collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical lattices. A generalization for a two-dimensional system is briefly considered.
Извор:
Physical Review E, 2013, 88, 3Финансирање / пројекти:
- Фотоника микро и нано структурних материјала (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-45010)
DOI: 10.1103/PhysRevE.88.032905
ISSN: 1539-3755
PubMed: 24125323
WoS: 000324055400010
Scopus: 2-s2.0-84885130168
Колекције
Институција/група
VinčaTY - JOUR AU - Gligorić, Goran AU - Maluckov, Aleksandra AU - Hadžievski, Ljupčo AU - Malomed, Boris A. PY - 2013 UR - https://vinar.vin.bg.ac.rs/handle/123456789/5667 AB - We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF) onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete bright solitons, which do not exist in lattices with the spatially uniform SDF nonlinearity. The UnST solitons coexist with stable staggered (ST) localized modes, which are always possible under the defocusing onsite nonlinearity. The results are obtained in a numerical form and also by means of variational approximation (VA). In the semi-infinite (truncated) system, some solutions for the UnST surface solitons are produced in an exact form. On the contrary to surface discrete solitons in uniform truncated lattices, the threshold value of the norm vanishes for the UnST solitons in the present system. Stability regions for the novel UnST solitons are identified. The same results imply the existence of ST discrete solitons in lattices with the spatially growing self-focusing nonlinearity, where such solitons cannot exist either if the nonlinearity is homogeneous. In addition, a lattice with the uniform onsite SDF nonlinearity and exponentially decaying intersite coupling is introduced and briefly considered. Via a similar mechanism, it may also support UnST discrete solitons. The results may be realized in arrayed optical waveguides and collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical lattices. A generalization for a two-dimensional system is briefly considered. T2 - Physical Review E T1 - Discrete localized modes supported by an inhomogeneous defocusing nonlinearity VL - 88 IS - 3 DO - 10.1103/PhysRevE.88.032905 ER -
@article{ author = "Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.", year = "2013", abstract = "We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF) onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete bright solitons, which do not exist in lattices with the spatially uniform SDF nonlinearity. The UnST solitons coexist with stable staggered (ST) localized modes, which are always possible under the defocusing onsite nonlinearity. The results are obtained in a numerical form and also by means of variational approximation (VA). In the semi-infinite (truncated) system, some solutions for the UnST surface solitons are produced in an exact form. On the contrary to surface discrete solitons in uniform truncated lattices, the threshold value of the norm vanishes for the UnST solitons in the present system. Stability regions for the novel UnST solitons are identified. The same results imply the existence of ST discrete solitons in lattices with the spatially growing self-focusing nonlinearity, where such solitons cannot exist either if the nonlinearity is homogeneous. In addition, a lattice with the uniform onsite SDF nonlinearity and exponentially decaying intersite coupling is introduced and briefly considered. Via a similar mechanism, it may also support UnST discrete solitons. The results may be realized in arrayed optical waveguides and collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical lattices. A generalization for a two-dimensional system is briefly considered.", journal = "Physical Review E", title = "Discrete localized modes supported by an inhomogeneous defocusing nonlinearity", volume = "88", number = "3", doi = "10.1103/PhysRevE.88.032905" }
Gligorić, G., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2013). Discrete localized modes supported by an inhomogeneous defocusing nonlinearity. in Physical Review E, 88(3). https://doi.org/10.1103/PhysRevE.88.032905
Gligorić G, Maluckov A, Hadžievski L, Malomed BA. Discrete localized modes supported by an inhomogeneous defocusing nonlinearity. in Physical Review E. 2013;88(3). doi:10.1103/PhysRevE.88.032905 .
Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Discrete localized modes supported by an inhomogeneous defocusing nonlinearity" in Physical Review E, 88, no. 3 (2013), https://doi.org/10.1103/PhysRevE.88.032905 . .