Related papers: KdV-Volterra chain
The main object of this paper is to produce a deformation of the KdV hierarchy of partial differential equations. We construct this deformation by taking a certain limit of the Toda hierarchy. This construction also provides a deformation…
There exist two versions of the Kadomtsev-Petviashvili equation, related to the Cartesian and cylindrical geometries of the waves. In this paper we derive and study a new version, related to the elliptic cylindrical geometry. The derivation…
We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a…
We show that the KdV6 equation recently studied in [1,2] is equivalent to the Rosochatius deformation of KdV equation with self-consistent sources (RD-KdVESCS) recently presented in [9]. The $t$-type bi-Hamiltonian formalism of KdV6…
Classification of the Egorov hydrodynamic chain and corresponding 2+1 quasilinear system is given in the previous paper. In this paper we present a general construction of explicit solutions for the WDVV equation associated with Hamiltonian…
The aim of this work is to present, in self-contained form, results concerning fundamental and the most important questions related to linear stochastic Volterra equations of convolution type. The paper is devoted to study the existence and…
The Volterra integral equations of the first kind with piecewise smooth kernel are considered. Such equations appear in the theory of optimal control of the evolving systems. The existence theorems are proved. The method for constructing…
We introduce integrable KdV type hierarchy associated naturally with arbitrary semi-simple Frobenius manifold. We present hierarchy in a Lax form and show that it admits bihamiltonian description.
A nonlocal form of a two-layer fluid system is proposed by a simple symmetry reduction, then by applying multiple scale method to it a general nonlocal two place variable coefficient modified KdV (VCmKdV) equation with shifted space and…
In 70's there was discovered a construction how to attach to some algebraic-geometric data an infinite-dimensional subspace in the space k((z)) of the Laurent power series. The construction was successfully used in the theory of integrable…
The Pluecker relations are equations which describe decomposable multivectors in $\bigwedge V$. We review all known versions, give some new ones, and decompose them into irreducible parts for the $GL(V)$-representations.
We introduce a hierarchy of mutually commuting dynamical systems on a finite number of Laurent series. This hierarchy can be seen as a prolongation of the KP hierarchy, or a ``reduction'' in which the space coordinate is identified with an…
We consider a Lie algebra generalizing the Virasoro algebra to the case of two space variables. We study its coadjoint representation and calculate the corresponding Euler equations. In particular, we obtain a bi-Hamiltonian system that…
We study higher order KdV equations from the GL(2,$\mathbb{R}$) $\cong$ SO(2,1) Lie group point of view. We find elliptic solutions of higher order KdV equations up to the ninth order. We argue that the main structure of the…
The contraction is applied to obtaining of integrable systems associated with nonsemisimple algebras. The effect of contraction is splitting off some components from initial system without loss of integrability.
Some forms of qKdV type equations are indicated which arise from Virasoro considerations.
We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense (in the spirit of [18]) and which remain close to multi-solitons. We show that these solutions are necessarily pure…
We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian structure of the dispersionless KdV…
Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution defined via reduction of the Toda lattice…
A new approach to integrability of affine Toda field theories and closely related to them KdV hierarchies is proposed. The flows of a hierarchy are explicitly identified with infinitesimal action of the principal abelian subalgebra of the…