A geometric study of the dispersionless Boussinesq type equation

Details A geometric study of the dispersionless Boussinesq type equation A geometric study of the dispersionless Boussinesq type equation

2005-11-06

arxiv.org/abs/nlin/0511012v1

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

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.1007/s10440-006-9034-5

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 . 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.

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