Geodesic
Propagation of discrete-temporal vortices in a waveguide array
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 149 (2007) no. 1, pp. 97-101

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In our work we theoretically study spatio-temporal vortices propagation in waveguide array. Approximation of weakly coupled waveguides and a linear waveguide model used to describe waveguide array. Major focus in our work dedicated to influence of array discreteness on dislocations propagation dynamics. We analyzed vortices with low topological charge. Discrepancies in propagation of wide and narrow impulse beams, associated with array discreteness, were revealed. Extreme narrow impulse propagation caused new dislocations born. With increasing vortex width effect of dislocations birth vanishes and only a simple type transformation from phase to mixed edge-screw is occurred. 
@article{UZKU_2007_149_1_a14,
     author = {A. K. Satarin and A. P. Sukhorukov},
     title = {Propagation of discrete-temporal vortices in a~waveguide array},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {97--101},
     publisher = {mathdoc},
     volume = {149},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2007_149_1_a14/}
}
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A. K. Satarin; A. P. Sukhorukov. Propagation of discrete-temporal vortices in a waveguide array. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 149 (2007) no. 1, pp. 97-101. http://geodesic.mathdoc.fr/item/UZKU_2007_149_1_a14/