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This article is cited in 3 scientific papers (total in 3 papers)
Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations
B. G. Konopelchenkoa, L. Martínez Alonsob, E. Medinac a 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.
Citation:
B. G. Konopelchenko, L. Martínez Alonso, E. Medina, “Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations”, TMF, 168:1 (2011), 125–137; Theoret. and Math. Phys., 168:1 (2011), 963–973
Linking options:
https://www.mathnet.ru/eng/tmf6668https://doi.org/10.4213/tmf6668 https://www.mathnet.ru/eng/tmf/v168/i1/p125
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Abstract page: | 497 | Full-text PDF : | 173 | References: | 81 | First page: | 9 |
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