TY - JOUR
T1 - Collapse arrest and soliton stabilization in nonlocal nonlinear media
AU - Bang, Ole
AU - Krolikowski, Wieslaw
AU - Wyller, John
AU - Rasmussen, Jens Juul
PY - 2002/10/24
Y1 - 2002/10/24
N2 - We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrödinger type equation. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric and have a positive definite Fourier spectrum, but can otherwise be of completely arbitrary shape and degree of nonlocality. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.
AB - We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrödinger type equation. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric and have a positive definite Fourier spectrum, but can otherwise be of completely arbitrary shape and degree of nonlocality. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.
UR - http://www.scopus.com/inward/record.url?scp=41349096194&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.66.046619
DO - 10.1103/PhysRevE.66.046619
M3 - Article
SN - 2470-0045
VL - 66
SP - 5
JO - Physical Review E
JF - Physical Review E
IS - 4
ER -