Geodesic
Singular sectors of the~one-layer Benney and dispersionless Toda systems and their interrelations
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 125-137

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We completely describe the singular sectors of the one-layer Benney system (classical long-wave equation) and dispersionless Toda system. The associated Euler–Poisson–Darboux equations $E(1/2,1/2)$ and $E(-1/2,-1/2)$ are the main tool in the analysis. We give a complete list of solutions of the one-layer Benney system depending on two parameters and belonging to the singular sector. We discuss the relation between Euler–Poisson–Darboux equations $E(\varepsilon,\varepsilon)$ with the opposite sign of $\varepsilon$.
Keywords: critical point, singular sector
Mots-clés : Euler–Poisson–Darboux equation. 
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     author = {B. G. Konopelchenko and L. Mart{\'\i}nez Alonso and E. Medina},
     title = {Singular sectors of the~one-layer {Benney} and dispersionless {Toda} systems and their interrelations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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B. G. Konopelchenko; L. Martínez Alonso; E. Medina. Singular sectors of the~one-layer Benney and dispersionless Toda systems and their interrelations. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 125-137. http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a9/