2,371 research outputs found

    Transformations of integrable hydrodynamic chains and their hydrodynamic reductions

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    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

    Integrable Dispersive Chains and Energy Dependent Schrodinger Operator

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    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

    Integrable hydrodynamic chains

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    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

    The Kupershmidt hydrodynamic chains and lattices

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    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

    The Hamiltonian approach in classification and integrability of hydrodynamic chains

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    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

    Explicit solutions of the WDVV equation determined by the "flat" hydrodynamic reductions of the Egorov hydrodynamic chains

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    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

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    Various links connecting well-known hydrodynamic chains and corresponding 2+1 nonlinear equations are described

    Integrability of the Egorov hydrodynamic type systems

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    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 associated with Dorfman Poisson brackets

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    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

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    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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