A Geometric Study of the Dispersionless Boussinesq Type Equation

2005/11/06 by Paul Kersten, P.H.M. Kersten, Iosif Krasil'shchik +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1007/s10440-006-9034-5

published as Acta Appl. Math. 90 (2006), 143-178

arxiv created 2005/11/06 · openalex publication_date 2006/05/29 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

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 <http://dx.doi.org/doi:10.1088/0305-4470/27/1/013>. 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.

Citations

• Homological Methods in Equations of Mathematical Physics
• (Non)local Hamiltonian and symplectic structures, recursions and hierarchies: a new approach and applications to theN= 1 supersymmetric KdV equation

Cited by

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