Explicit solutions of an integrable boundary value problem for the two-dimensional Toda lattice

V. L. Vereshchagin

Institute of Mathematics with Computing Center, Ufa Science Center, RAS, Ufa, Russia

Abstract: We obtain an explicit solution of the integrable boundary value problem for the two-dimensional Toda lattice using the inverse scattering method. We interpret the integrability property in terms of the corresponding linear problem, the Gel'fand–Levitan–Marchenko equation, and the dressing procedure. The simplest initial solutions of the boundary value problem become new nontrivial solutions after the dressing procedure is applied.

Keywords: Toda chain, integrable boundary value problem, dressing procedure.

Received: 01.02.2010

DOI: 10.4213/tmf6561

 English version: Theoretical and Mathematical Physics, 2010, 165:1, 1256–1261

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