A class of integro-differential equations constrained from the KP hierarchy

Abstract

In this paper we give a class of integro-differential evolution equations which generalizes the ILWk hierarchy. We show the generalized Lax pairs, the bilinear representations and the rational and N-soliton solutions for these integro-differential equations. We also give the Hamiltonian formalism for the simplest set of equations among these integro-differential equations, which is the coupling of the ILW equation and the time-dependent Schrodinger equations.