TY - JOUR
T1 - Stable two-dimensional soliton supported by a local nonlinearity
AU - Granot, Er’el
AU - Malomed, Boris A.
PY - 2000
Y1 - 2000
N2 - We show that an attractive nonlinear potential in the form of a modified Azbel two-dimensional (2D) δ function (that, unlike the traditional 2D δ function, gives rise to a well-defined bound state in quantum mechanics) supports a 2D localized state (“soliton”), that may be stable according to the Vakhitov-Kolokolov (VK) criterion, provided that the soliton’s amplitude is not too small. A direct, although not general, dynamical stability consideration yields results in compliance with the VK criterion.
AB - We show that an attractive nonlinear potential in the form of a modified Azbel two-dimensional (2D) δ function (that, unlike the traditional 2D δ function, gives rise to a well-defined bound state in quantum mechanics) supports a 2D localized state (“soliton”), that may be stable according to the Vakhitov-Kolokolov (VK) criterion, provided that the soliton’s amplitude is not too small. A direct, although not general, dynamical stability consideration yields results in compliance with the VK criterion.
UR - http://www.scopus.com/inward/record.url?scp=16644382495&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.62.2185
DO - 10.1103/PhysRevB.62.2185
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AN - SCOPUS:16644382495
SN - 1098-0121
VL - 62
SP - 2185
EP - 2187
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 3
ER -