Explicit solutions of an~integrable boundary value problem for the~two-dimensional Toda lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 1, pp. 25-31
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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.
@article{TMF_2010_165_1_a1,
author = {V. L. Vereshchagin},
title = {Explicit solutions of an~integrable boundary value problem for the~two-dimensional {Toda} lattice},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {25--31},
publisher = {mathdoc},
volume = {165},
number = {1},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2010_165_1_a1/}
}
TY - JOUR AU - V. L. Vereshchagin TI - Explicit solutions of an~integrable boundary value problem for the~two-dimensional Toda lattice JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2010 SP - 25 EP - 31 VL - 165 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2010_165_1_a1/ LA - ru ID - TMF_2010_165_1_a1 ER -
%0 Journal Article %A V. L. Vereshchagin %T Explicit solutions of an~integrable boundary value problem for the~two-dimensional Toda lattice %J Teoretičeskaâ i matematičeskaâ fizika %D 2010 %P 25-31 %V 165 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2010_165_1_a1/ %G ru %F TMF_2010_165_1_a1
V. L. Vereshchagin. Explicit solutions of an~integrable boundary value problem for the~two-dimensional Toda lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 1, pp. 25-31. http://geodesic.mathdoc.fr/item/TMF_2010_165_1_a1/