相关论文: Integrable hydrodynamic chains
Using the method of hydrodynamic reductions, we find all integrable infinite (1+1)-dimensional hydrodynamic-type chains of shift one. A class of integrable infinite (2+1)-dimensional hydrodynamic-type chains is constructed.
A new approach extracting multi-parametric hydrodynamic reductions for the integrable hydrodynamic chains is presented. The Benney hydrodynamic chain is considered.
New approach to classification of integrable hydrodynamic chains is established. Generating functions of conservation laws are classified by the method of hydrodynamic reductions. N parametric family of explicit hydrodynamic reductions…
New approach in classification of integrable hydrodynamic chains is established. This is the method of the Hamiltonian hydrodynamic reductions. Simultaneously, this approach yields explicit Hamiltonian hydrodynamic reductions of the…
Hydrodynamic reductions of the hydrodynamic chain associated with dispersionless limit of 2+1 Harry Dym equation are found by the Miura type and reciprocal transformations applied to the Benney hydrodynamic chain.
The diagonal hydrodynamic reductions of a hierarchy of integrable hydrodynamic chains are explicitly characterized. Their compatibility with previously introduced reductions of differential type is analyzed and their associated class of…
A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable…
In this paper we consider a new class of Hamiltonian hydrodynamic type systems, whose conservation laws are polynomial with respect to one of field variables.
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden…
We describe the results that have so far been obtained in the classification problem for integrable (2+1)-dimensional systems of hydrodynamic type. The systems of Gibbons--Tsarev type are the most fundamental here. A whole class of…
A complete classification of integrable conservative hydrodynamic chains is presented. These hydrodynamic chains are written via special coordinates -- moments, such that right hand sides of these infinite component systems depend linearly…
Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 2-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type…
Various links connecting well-known hydrodynamic chains and corresponding 2+1 nonlinear equations are described.
The new integrable hydrodynamic equations obtained for WZNW model with $SU(2)$, $SO(3)$, $SP(2)$ and $SU(\infty )$ constant torsions
The first example of the so-called "coupled" integrable hydrodynamic chain is presented. Infinitely many commuting flows are derived. Compatibility conditions of the first two of them lead to the remarkable Manakov--Santini system.…
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable…
The particular case of the integrable two component (2+1)-dimensional hydrodynamical type systems, which generalises the so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A…
This paper develops a geometric approach to the theory of integrability by hydrodynamic reductions to establish an equivalence, for a large class of quasilinear systems, between hydrodynamic integrability and the existence of nets…
We construct integrable pseudopotentials with an arbitrary number of fields in terms of generalized hypergeometric functions. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic type systems. An interesting class of…
We construct a family of integrable hydrodynamic type systems with three independent and n>1 dependent variables in terms of solutions of linear system of PDEs with rational coefficients. We choose the existence of a pseudopotential as a…