420 citations · 1k across the 45 of their papers we have counts for
46 papers
Self-similar asymptotics in the decay problem for the Volterra lattice with zero boundary condition
V. E. Adler, B. I. Suleimanov
The article is devoted to the problem of decay of initial stationary state for the Volterra lattice with zero boundary condition. We show that this process is asymptotically self-s…
Vector systems of Painlevé type
V. E. Adler, V. V. Sokolov
The group reduction procedure is applied to vector generalizations of the NLS, mKdV, and KdV equations. The resulting ODE systems admit isomonodromic Lax representations and are mu…
Spinning top in quadratic potential and matrix dressing chain
V. E. Adler, A. P. Veselov
We show that the equations of motion of the rigid body about centre of mass in the Newtonian field with a quadratic potential are special reductions of period-one closure of the Da…
3D-consistency of negative flows
V. E. Adler
We study the 3D-consistency property for negative symmetries of KdV type equations. Its connection with the 3D-consistency of discrete equations is explained.
Negative flows for several integrable models
V. E. Adler
A construction of negative flows for integrable systems based on the Lax representation and squared eigenfunctions is proposed. Examples considered include the Boussinesq equation…
Negative flows and non-autonomous reductions of the Volterra lattice
V. E. Adler
We study reductions of the Volterra lattice corresponding to stationary equations for the additional, noncommutative subalgebra of symmetries. It is shown that, in the case of gene…