2,108 research outputs found
Integrable Dispersive Chains and Energy Dependent Schrodinger Operator
In this paper we consider integrable dispersive chains associated with the so
called Energy Dependent Schrodinger operator. In a general case multi component
reductions of these dispersive chains are new integrable systems, which are
characterised by two arbitrary natural numbers. Also we show that integrable
three dimensional linearly degenerate quasilinear equations of a second order
possess infinitely many differential constraints. Corresponding dispersive
reductions are integrable systems associated with the Energy Dependent
Schrodinger operator
Transformations of integrable hydrodynamic chains and their hydrodynamic reductions
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 Kupershmidt hydrodynamic chains and lattices
This paper is devoted to the very important class of hydrodynamic chains
first derived by B. Kupershmidt and later re-discovered by M. Blaszak. An
infinite set of local Hamiltonian structures, hydrodynamic reductions
parameterized by the hypergeometric function and reciprocal transformations for
the Kupershmidt hydrodynamic chains are described
Explicit solutions of the WDVV equation determined by the "flat" hydrodynamic reductions of the Egorov hydrodynamic chains
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 hydrodynamic reductions of these Egorov hydrodynamic chain
Modified dispersionless Veselov--Novikov equations and corresponding hydrodynamic chains
Various links connecting well-known hydrodynamic chains and corresponding 2+1
nonlinear equations are described
The Hamiltonian approach in classification and integrability of hydrodynamic chains
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 Hamiltonian hydrodynamic chains. The concept of reducible
Poisson brackets is established. Also this approach is useful for
non-Hamiltonian hydrodynamic chains. The deformed Benney hydrodynamic chain is
considered
Integrability of the Egorov hydrodynamic type systems
Integrability criterion for the Egorov hydrodynamic type systems is
presented. The general solution by generalized hodograph method is found.
Examples are give
Integrable hydrodynamic chains
A new approach for derivation of Benney-like momentum chains and integrable
hydrodynamic type systems is presented. New integrable hydrodynamic chains are
constructed, all their reductions are described and integrated. New (2+1)
integrable hydrodynamic type systems are found.Comment: WARWICK CONFERENCE 2002 Geometry & Mechanics I
Integrable hydrodynamic chains associated with Dorfman Poisson brackets
This paper is devoted to a description of integrable Hamiltonian hydrodynamic
chains associated with Dorfman Poisson brackets. Three main classes of these
hydrodynamic chains are selected. Generating functions of conservation laws and
commuting flows are found. Hierarchies of these Hamiltonian hydrodynamic chains
are extended on negative moments and negative time variables. Corresponding
three dimensional quasilinear equations of the second order are presented
New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems
New Hamiltonian formalism based on the theory of conjugate curvilinear
coordinate nets is established. All formulas are ``mirrored'' to corresponding
formulas in the Hamiltonian formalism constructed by B.A. Dubrovin and S.P.
Novikov (in a flat case) and E.V. Ferapontov (in a non-flat case). In the
``mirrored-flat'' case the Lagrangian formulation is found. Multi-Hamiltonian
examples are presented. In particular Egorov's case, generalizations of local
Nutku--Olver's Hamiltonian structure and corresponding Sheftel--Teshukov's
recursion operator are presented. An number of Hamiltonian structures of all
odd orders is found
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