par Loris, Ignace ;Willox, R.
Référence Structure and dynamics of complex systems (29-30/9/1997: Alden-Biesen, Belgium)
Publication Non publié, 1997
Communication à un colloque
Résumé : The Kadomtsev-Petviashvili (KP) equation is the most fundamental example of an integrable evolution equation with infinitely many degrees of freedom. As an integrable equation it possesses all the features such systems are known to exhibit (bi-Hamiltonian structure and the related infinite amount of conserved densities and symmetries etc.). It is common knowledge that numerous well-known 1+1 dimensional soliton systems can be obtained as dimensional reductions of the KP-equation (e.g.: the KdV or Boussinesq equations). As opposed to these, we are interested in certain non-standard symmetry reductions of the KP-equation, implemented by the introduction of $2m$ auxiliary dependent variables (satisfying the (adjoint) KP linear problem) and relating them with the KP Lax-operator. We shall investigate how these constraints may be adapted to the case of non-vanishing boundary conditions (for the auxiliary fields).