HAMILTONIAN STRUCTURES FOR THE GENERALIZED DISPERSIONLESS KdV HIERARCHY
نویسندگان
چکیده
منابع مشابه
Hamiltonian Structures for the Generalized Dispersionless Kdv Hierarchy
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and third Hamiltonian structures are calculated directly from the r-matrix approach. Since the third structure is not related recursively with the first two ones ...
متن کاملLagrangian Approach to Dispersionless KdV Hierarchy
We derive a Lagrangian based approach to study the compatible Hamiltonian structure of the dispersionless KdV and supersymmetric KdV hierarchies and claim that our treatment of the problem serves as a very useful supplement of the so-called r-matrix method. We suggest specific ways to construct results for conserved densities and Hamiltonian operators. The Lagrangian formulation, via Noether’s ...
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An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is obtained via hodograph transformation. Furthermore, the dispersionless Gelfand-Dickey hierarchy with sources (dGDHWS) is presented. PACS number: 02. 03. Ik
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The r-KdV-CH hierarchy is a generalization of the Korteweg-de Vries and Camassa-Holm hierarchies parametrized by r + 1 constants. In this paper we clarify some properties of its multi-Hamiltonian structures, prove the semisimplicity of the associated bihamiltonian structures and the formula for their central invariants. By introducing a class of generalized Hamiltonian structures, we give in a ...
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ژورنال
عنوان ژورنال: Reviews in Mathematical Physics
سال: 1996
ISSN: 0129-055X,1793-6659
DOI: 10.1142/s0129055x96000378