A geometric study of the dispersionless Boussinesq type equation
Abstract
We discuss the dispersionless Boussinesq type equation, which is equivalent to the BenneyLax equation, being a system of equations of hydrodynamical type. This equation was discussed in <http://dx.doi.org/doi:10.1088/03054470/27/1/013>. 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 infinitedimensional algebra of recursion operators.
 Publication:

arXiv eprints
 Pub Date:
 November 2005
 arXiv:
 arXiv:nlin/0511012
 Bibcode:
 2005nlin.....11012K
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics
 EPrint:
 Acta Appl. Math. 90 (2006), 143178