107 citations · 289 across the 15 of their papers we have counts for
15 papers
Some exact solutions of the Volterra lattice
V. E. Adler, A. B. Shabat
We study solutions of the Volterra lattice satisfying the stationary equation for its non-autonomous symmetry. It is shown that the dynamics in and are governed by the cont…
Volterra chain and Catalan numbers
V. E. Adler, A. B. Shabat
We consider the Cauchy problem for the Volterra chain with an initial condition equal to 0 in one node and 1 in the others. It is shown that this problem admits an exact solution i…
Towards the theory of integrable hyperbolic equations of third order
V. E. Adler, A. B. Shabat
The examples are considered of integrable hyperbolic equations of third order with two independent variables. In particular, an equation is found which admits as evolutionary symme…
Computable Integrability
Alexey Shabat, Elena Kartashova
This is a preliminary version of the textbook on integrable systems. The work has been partly supported by Grant Nr.10/2006-RU, Austrian Academic Exchange Service ÖAD and Grant P20…
The model equation of soliton theory
V. E. Adler, A. B. Shabat
We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on…
On the One Class of Hyperbolic Systems
Vsevolod E. Adler, Alexey B. Shabat
The classification problem is solved for some type of nonlinear lattices. These lattices are closely related to the lattices of Ruijsenaars-Toda type and define the Backlund auto-t…