zbMATH — the first resource for mathematics

Soliton solutions of an integrable boundary problem on the half-line for the discrete Toda chain. (English) Zbl 1177.37077
Theor. Math. Phys. 148, No. 3, 1199-1209 (2006); translation from Teor. Mat. Fiz. 148, No. 3, 387-397 (2006).
Summary: 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) 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.
37K60 Lattice dynamics; integrable lattice equations
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
Full Text: DOI
[1] F. Date, M. Jimbo, and T. Miwa, J. Phys. Soc. Japan., 51, 4116–4124, 4125–4131 (1982); 52, 761–765, 766–771 (1983). · doi:10.1143/JPSJ.51.4116
[2] Yu. B. Suris, Leningr. Math. J., 2, 339–352 (1991).
[3] T. G. Kazakova, Theor. Math. Phys., 138, 356–369 (2004). · Zbl 1178.37078 · doi:10.1023/B:TAMP.0000018452.62337.c8
[4] T. G. Kazakova, ”Finite-dimensional reductions of discrete systems [in Russian],” PhD thesis, Inst. Math. Comput. Ctr., Ufa Sci. Ctr., Russ. Acad. Sci., Ufa (2005).
[5] I. T. Habibullin and T. G. Kazakova, J. Phys. A, 34, 10369–10376 (2001).
[6] V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Problem Method [in Russian], Nauka, Moscow (1980); English transl.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method, Plenum, New York (1984). · Zbl 0598.35002
[7] I. T. Habibullin, Theor. Math. Phys., 114, 90–115 (1998). · Zbl 0946.35089 · doi:10.1007/BF02557111
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.