The improved Boussinesq equation is studied in this paper. Control properties for this equation posed on a bounded interval are first considered. When the control acts through the Dirichlet boundary condition the linearized system is proved to be approximately but not spectrally controllable. In a second part, the equation is posed on the one-dimensional torus and distributed moving controls ar...

A. general theory for determining Hamiltonian model equations from noncanonical perturbation expansions of Hamiltonian systems is applied to the Boussinesq expan sion fcr long, small amplitude waves in shallow water, leading to the Korteweg-deVries equation. New Hamiltonian model equations, including a natural "Hamiltonian ver-cn» of the KdV equation, are proposed. The method also provides a di...

We construct new integrable coupled systems of N = 1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian struct...