A geometric study of the dispersionless Boussinesq type equation

P.H.M. Kersten; I. Krasil'shchik; A. Verbovetsky

doi:10.1007/s10440-006-9034-5

A geometric study of the dispersionless Boussinesq type equation

P.H.M. Kersten, I. Krasil'shchik, A. Verbovetsky

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Abstract

We discuss the dispersionless Boussinesq type equation, which is equivalent to the Benney–Lax equation, being a system of equations of hydrodynamical type. This equation was discussed in [4]. The results include: A description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws (cosymmetries). Highly interesting are the appearances of operators that send conservation laws and symmetries to each other but are neither Hamiltonian, nor symplectic. These operators give rise to a noncommutative infinite-dimensional algebra of recursion operators.

Original language	English
Pages (from-to)	143-178
Number of pages	36
Journal	Acta applicandae mathematicae
Volume	90
Issue number	1-2
DOIs	https://doi.org/10.1007/s10440-006-9034-5
Publication status	Published - 2006

Keywords

MSC-35Q53
MSC-37K05

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10.1007/s10440-006-9034-5

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AU - Kersten, P.H.M.

AU - Krasil'shchik, I.

AU - Verbovetsky, A.

PY - 2006

Y1 - 2006

N2 - We discuss the dispersionless Boussinesq type equation, which is equivalent to the Benney–Lax equation, being a system of equations of hydrodynamical type. This equation was discussed in [4]. The results include: A description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws (cosymmetries). Highly interesting are the appearances of operators that send conservation laws and symmetries to each other but are neither Hamiltonian, nor symplectic. These operators give rise to a noncommutative infinite-dimensional algebra of recursion operators.

AB - We discuss the dispersionless Boussinesq type equation, which is equivalent to the Benney–Lax equation, being a system of equations of hydrodynamical type. This equation was discussed in [4]. The results include: A description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws (cosymmetries). Highly interesting are the appearances of operators that send conservation laws and symmetries to each other but are neither Hamiltonian, nor symplectic. These operators give rise to a noncommutative infinite-dimensional algebra of recursion operators.

KW - MSC-35Q53

KW - MSC-37K05

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EP - 178

JO - Acta applicandae mathematicae

JF - Acta applicandae mathematicae

IS - 1-2

ER -

A geometric study of the dispersionless Boussinesq type equation

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