Asymptotics of discrete orthogonal polynomials and the continuum limit of the Toda lattice (Q2773091)

The authors consider the continuum limit of the Toda lattice, that is, they consider the system of partial differential equations in \(a(x,t)\) and \(b(x,t)\) (or the equivalent system in the variables \(\alpha=a-2b\), \(\beta=a+2b\)) \(\partial a /\partial t = (2b) \partial b /\partial x\), \(\partial b /\partial t = (b/2) \partial a /\partial x\), subject to the initial conditions \(a(x,0)=a(x)\), \(b(x,0)=b(x)\), and boundary conditions \(b(0,t)=b(1,t)=0\). Their approach is based on the analytic theory of discrete orthogonal polynomials. This is in contrast to the perturbation techniques used by other authors.