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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.
MSC:
37K60 Lattice dynamics; integrable lattice equations
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
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