Bi-Hamiltonian structures of d-Boussinesq and Benney-Lax equations
نویسندگان
چکیده
منابع مشابه
Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
The bi-Hamiltonian structure of certain multi-component integrable systems, generalizations of the dispersionless Toda hierarchy, is studied for systems derived from a rational Lax function. One consequence of having a rational rather than a polynomial Lax functions is that the corresponding bi-Hamiltonian structures are degenerate, i.e. the metric which defines the Hamiltonian structure has va...
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Methods in Riemann–Finsler geometry are applied to investigate bi–Hamiltonian structures and related mKdV hierarchies of soliton equations derived geometrically from regular Lagrangians and flows of non–stretching curves in tangent bundles. The total space geometry and nonholonomic flows of curves are defined by Lagrangian semisprays inducing canonical nonlinear connections (N–connections), Sas...
متن کاملThe D-boussinesq Equation: Hamiltonian and Symplectic Structures; Noether and Inverse Noether Operators
Using new methods of analysis of integrable systems,based on a general geometric approach to nonlinear PDE,we discuss the Dispersionless Boussinesq Equation, which is equivalent to the Benney-Lax equation,being a system of equations of hydrodynamical type. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of co...
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A bi-Hamiltonian structure is a pair of Poisson structures P , Q which are compatible, meaning that any linear combination αP+βQ is again a Poisson structure. A biHamiltonian structure (P,Q) is called flat if P and Q can be simultaneously brought to a constant form in a neighborhood of a generic point. We prove that a generic biHamiltonian structure (P,Q) on an odd-dimensional manifold is flat ...
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where P+ is a differential operator whose coefficients are differential polynomials in u, that is, polynomials in u and its x-derivatives u (s~. (The subscript + may be ignored at this point: we introduce it so as not to conflict with the notation in the main body of the paper.) Since L, is an operator of order zero, for (1.2) to make sense P, must be chosen so that the commutator on the right ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1994
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/27/1/013