The Toda lattice with step-like initial data. Soliton asymptotics. (English) Zbl 0958.35132
Summary: We study the asymptotic behaviour of solutions of the Toda lattice Cauchy problem with step-like initial data near the wavefront. The initial data are supposed to tend to the discrete Laplacian on one half-axis and to the periodic Jacobi matrix on the other. The solution is shown to split into an infinite series of solitons when time tends to infinity. We obtain an exact asymptotic formula for these solutions.
MSC:
35Q58 | Other completely integrable PDE (MSC2000) |
37K60 | Lattice dynamics; integrable lattice equations |
37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |