Soliton solutions of an integrable boundary problem on the half-line for the discrete Toda chain

V. L. Vereshchagin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: We write formulas for soliton solutions of the discrete Toda chain and pose the integrable boundary value problem for this chain. We find conditions for the parameters {(}discrete spectrum points, transmission coefficients, and the corresponding factors{\rm)} whereby solutions of the integrable boundary value problem are selected from all soliton solutions. As a result, we construct two hierarchies of soliton solutions of the specified problem with even and odd soliton numbers and find an explicit form of the conditions for the parameters.

Keywords: discrete Toda chain, integrable boundary value problem, soliton.

Received: 02.02.2006

DOI: 10.4213/tmf2323

 English version: Theoretical and Mathematical Physics, 2006, 148:3, 1199–1209

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