# A solution of the initial value problem for half-infinite integrable lattice systems

Common, Alan K. (1992) A solution of the initial value problem for half-infinite integrable lattice systems. Inverse Problems, 8 (3). pp. 393-408. ISSN 0266-5611. (doi:10.1088/0266-5611/8/3/003) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:23270)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. Official URLhttp://dx.doi.org/10.1088/0266-5611/8/3/003

## Abstract

In previous studies solutions of a number of half-infinite nonlinear lattice systems were constructed from continued fraction solutions to corresponding Riccati equations. A method for linearizing the Kac-Van Moerbeke lattice equations was reconstructed and extended to the discrete nonlinear Schrodinger equation, relativistic Toda lattice equations as well as other examples. This approach demonstrated the important role played by the boundary condition at the finite end and solutions were obtained for given behaviour of this end with time. Here the initial value problem will be solved, i.e. we will obtain solutions of these half-infinite lattice equations corresponding to prescribed values at t = 0. Such solutions were obtained for the Kac-Van Moerbeke lattice through studying the time behaviour of continued fractions related to Jacobi matrices and the corresponding 'hamburger moment problem'. A similar approach is used here and we find for the discrete nonlinear Schrodinger equation that the continued fractions which arise are related to the 'trigonometric moment problem'. We also consider the discrete modified KdV equation, relativistic Toda lattice and discrete-time Toda lattices and in these cases T-fractions, which are related to the 'strong Stieltjes moment problem', are used to solve the initial value problem.

Item Type: Article 10.1088/0266-5611/8/3/003 Q Science > QA Mathematics (inc Computing science)Q Science > QC Physics Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science A. Xie 01 Nov 2009 00:05 UTC 16 Nov 2021 10:01 UTC https://kar.kent.ac.uk/id/eprint/23270 (The current URI for this page, for reference purposes)