Abstract:
We examine the Cauchy problem for a semi-infinite Volterra chain with an asymptotically periodic initial condition. The question is addressed of existence of a solution with the same asymptotics at infinity as the initial condition. We demonstrate that the method of the inverse scattering problem is applicable to this problem.
Keywords:Volterra chain, scattering problem, asymptotically periodic condition, inverse problem method, Cauchy problem, global solvability.