Singular sectors of the 1-layer Benney and dToda systems and their interrelations

Abstract

Complete description of the singular sectors of the 1-layer Benney system (classical long wave equation) and dToda system is presented. Associated Euler-Poisson-Darboux equations E(1/2,1/2) and E(-1/2,-1/2) are the main tool in the analysis. A complete list of solutions of the 1-layer Benney system depending on two parameters and belonging to the singular sector is given. Relation between Euler-Poisson-Darboux equations E(a,a) with opposite sign of a is discussed.

15 pages; Theor. Mathem. Physics, 2011

References in corpus (2)

• The double scaling limit method in the Toda hierarchy
• On the singular sector of the Hermitian random matrix model in the large N limit

Cited by in corpus (4)

• Quasi-classical approximation in vortex filament dynamics. Integrable systems, gradient catastrophe and flutter
• Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems
• Gradient catastrophe and flutter in vortex filament dynamics
• Unfolding of singularities and differential equations