A Nonlocal Kac-van Moerbeke Equation Admitting N-Soliton Solutions

Abstract

Using our previous work on reflectionless analytic difference operators and a nonlocal Toda equation, we introduce analytic versions of the Volterra and Kac-van Moerbeke lattice equations. The real-valued N-soliton solutions to our nonlocal equations correspond to self-adjoint reflectionless analytic difference operators with N bound states. A suitable scaling limit gives rise to the N-soliton solutions of the Korteweg-de Vries equation.