TY - JOUR
T1 - Multi-component vortex solutions in symmetric coupled nonlinear Schrödinger equations
AU - Desyatnikov, A. S.
AU - Pelinovsky, D. E.
AU - Yang, J.
N1 - Funding Information:
Acknowledgements. A.D. and D.P. are thankful to Yuri S. Kivshar for valuable discussions. This work was initiated during the visit of D.P. in the Australian National University in December 2004. The work of A.D. was supported by the Australian Research Council and the Australian National University. The work of D.P. was supported by the PREA and NSERC grants. The work of J.Y. was supported by the NSF.
PY - 2008/6
Y1 - 2008/6
N2 - A Hamiltonian system of incoherently coupled nonlinear Schrödinger (NLS) equations is considered in the context of physical experiments in photorefractive crystals and Bose-Einstein condensates. Due to the incoherent coupling, the Hamiltonian system has a group of various symmetries that include symmetries with respect to gauge transformations and polarization rotations. We show that the group of rotational symmetries generates a large family of vortex solutions that generalize scalar vortices, vortex pairs with either double or hidden charge, and coupled states between solitons and vortices. Novel families of vortices with different frequencies and vortices with different charges at the same component are constructed and their linearized stability problem is block-diagonalized for numerical analysis of unstable eigenvalues.
AB - A Hamiltonian system of incoherently coupled nonlinear Schrödinger (NLS) equations is considered in the context of physical experiments in photorefractive crystals and Bose-Einstein condensates. Due to the incoherent coupling, the Hamiltonian system has a group of various symmetries that include symmetries with respect to gauge transformations and polarization rotations. We show that the group of rotational symmetries generates a large family of vortex solutions that generalize scalar vortices, vortex pairs with either double or hidden charge, and coupled states between solitons and vortices. Novel families of vortices with different frequencies and vortices with different charges at the same component are constructed and their linearized stability problem is block-diagonalized for numerical analysis of unstable eigenvalues.
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U2 - 10.1007/s10958-008-9031-5
DO - 10.1007/s10958-008-9031-5
M3 - Article
AN - SCOPUS:49349100386
VL - 151
SP - 3091
EP - 3111
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 4
ER -