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TMF, 2010, Volume 165, Number 1, Pages 25–31 (Mi tmf6561)  

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

DOI: https://doi.org/10.4213/tmf6561

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

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Received: 01.02.2010

Citation: V. L. Vereshchagin, “Explicit solutions of an integrable boundary value problem for the two-dimensional Toda lattice”, TMF, 165:1 (2010), 25–31; Theoret. and Math. Phys., 165:1 (2010), 1256–1261

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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