Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and
cannot be solved analytically. Integrable systems lie on the other extreme. They possess …

For several classes of second-order dispersionless PDEs, we show that the symbols of their
formal linearizations define conformal structures that must be Einstein-Weyl in 3D (or self …

We introduce and study a new class of kinetic equations, which arise in the description of
nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between …

F u, ui, uij 0, 1 where u is a vector-function of d 1 independent variables. For definiteness, let
us consider (31)-dimesional PDEs in four independent variables t, x, y, z. Equations of this …

The integrability of an m-component system of hydrodynamic type, ut= V (u) ux, by the
generalized hodograph method requires the diagonalizability of the m× m matrix V (u). This …

We investigate integrable second-order equations of the form F(u_xx,u_xy,u_yy,u_xt,u_yt,
u_tt)=0, which typically arise as the Hirota-type relations for various (2+ 1)-dimensional …

Abstract Characteristic Lie rings for Toda and Volterra type (2+ 1)-dimensional lattices are
defined. Some properties of these rings are studied. Infinite sequence of special kind …

We demonstrate that SDYM (self-dual Yang-Mills) equations for the Lie algebra of one-
dimensional vector fields represent a natural reduction in the framework of a general linearly …

We characterize non-degenerate Lagrangians of the form such that the corresponding Euler-
Lagrange equations are integrable by the method of hydrodynamic reductions. The …

We investigate second-order quasilinear equations of the form fijuxixj= 0, where u is a
function of n independent variables x1,…, xn, and the coefficients fij depend on the first …