Geodesic
A class of multidimensional integrable hierarchies and their reductions
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 15-22

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We consider a class of multidimensional integrable hierarchies connected with the commutativity of general (unreduced) $(N+1)$-dimensional vector fields containing a derivative with respect to a spectral variable. These hierarchies are determined by a generating equation, equivalent to the Lax–Sato form. We present a dressing scheme based on a nonlinear vector Riemann problem for this class. As characteristic examples, we consider the hierarchies connected with the Manakov–Santini equation and the Dunajski system.
Keywords: integrable hierarchy, dispersionless equation, heavenly equation, dressing method. 
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     author = {L. V. Bogdanov},
     title = {A class of multidimensional integrable hierarchies and their reductions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {15--22},
     publisher = {mathdoc},
     volume = {160},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a1/}
}
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L. V. Bogdanov. A class of multidimensional integrable hierarchies and their reductions. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 15-22. http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a1/