On a numerically stable algorithm for the analysis of Generalized Volterra lattice

Abstract

Volterra or Langmuir lattice is the dynamical model where the interaction of particle with the nearest neighbors is taken into account. It is known since J. Moser that the analysis of the Volterra lattice is related with isospectral deformation of a tridiagonal Jacobi operator. The main numerical problem in this setting is the inverse spectral problem for this Jacobi operator. Generalized Volterra lattice is a dynamical model where the interaction of particle with some fixed number of neighbors is taken into account. This model is a particular case of the discrete KP equation. The analysis of discrete KP equation is related with a class of Hessenberg operators. In this chapter we propose and study a stable algorithm for the numerical solution of the inverse spectral problem for the band Hessenberg operator with application to the analysis of generalized Volterra lattice. © Springer Science+Business Media New York 2013.