Soliton asymptotics of the Cauchy problem solution for the Toda lattice. (English) Zbl 0872.35107
Summary: The solution of the Cauchy problem for the Toda lattice with step-like initial data is shown to split into an infinite series of solitons when time tends to infinity. An exact asymptotic formula for such solutions is obtained.
MSC:
35Q58 | Other completely integrable PDE (MSC2000) |
35C20 | Asymptotic expansions of solutions to PDEs |
35Q51 | Soliton equations |