Geodesic
Nonlocal symmetries in two-field divergent evolutionary systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 351-363

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We evaluate nonlocal symmetries for third-order exactly integrable two-field divergent evolutionary equations. These symmetries, regarded as evolutionary equations, commute with higher analogues of the underlying original equations and seem to be exactly integrable. By differentiating nonlocal systems and changing the variables, we obtain local hyperbolic systems and third-order nonevolutionary systems. We find a zero-curvature representation for some of the new systems.
Keywords: conserved density, weakly nonlocal variable, nonlocal symmetry, negative flow, exact integrability. 
@article{TMF_2008_156_3_a2,
     author = {A. G. Meshkov},
     title = {Nonlocal symmetries in two-field divergent evolutionary systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {351--363},
     publisher = {mathdoc},
     volume = {156},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a2/}
}
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A. G. Meshkov. Nonlocal symmetries in two-field divergent evolutionary systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 351-363. http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a2/