This article is cited in 3 papers

Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations

B. G. Konopelchenko^a, L. Martínez Alonso^b, E. Medina<sup>c

a</sup> Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy
^b Departamento de Física Teórica II, Universidad Complutense, Madrid, Spain
^c Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Cádiz, Spain

Abstract: 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, Euler–Poisson–Darboux equation.

DOI: 10.4213/tmf6668

 English version: Theoretical and Mathematical Physics, 2011, 168:1, 963–973

Bibliographic databases:

• 
• 
• 
•