Symmetries Of KP Hierarchy Research Articles

Conserved quantities and symmetries of KP hierarchy

Conserved quantities and symmetries of the KP equation from the point of view of the Sato theory that provides a unifying approach to soliton equations is studied. Conserved quantities are derived from the generalized Lax equations. Some reductions of the KP hierarchy such as KdV, Boussinesq, a coupled KdV, and Sawada–Kotera equation are also considered. By expansion of the squared eigenfunctions of the Lax equations in terms of the τ function, symmetries of the KP equations are obtained. The relationship of this procedure to the two-dimensional recursion operator newly found by Fokas and Santini is discussed.