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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 165, No. 1, pp. 25–31, October, 2010.
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Vereshchagin, V.L. Explicit solutions of an integrable boundary value problem for the two-dimensional toda lattice. Theor Math Phys 165, 1256–1261 (2010). https://doi.org/10.1007/s11232-010-0107-2
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DOI: https://doi.org/10.1007/s11232-010-0107-2