COMMUTING CHARGES OF THE QUANTUM KORTEWEG-DE VRIES AND BOUSSINESQ THEORIES FROM THE REDUCTION OF W∞ AND W1+∞ ALGEBRAS

Integrability of the quantum Boussinesq equation for c=-2 is demonstrated by giving a recursive algorithm for generating explicit expressions for the infinite number of commuting charges based on a reduction of the W∞-algebra. These charges exist for all spins s≥2. Likewise, reductions of the W∞/2- and W(1+∞)/2-algebras yield the commuting quantum charges for the quantum KdV equation at c= -2 and c=1/2, respectively.