Long-time asymptotics for Toda shock waves in the modulation region. (English) Zbl 1537.37063
The long-time asymptotics of Toda shock waves is studied. Proofs of asymptotic expansions of solutions are given, and the influence of resonances and eigenvalues on the leading terms of asymptotics is analyzed.
Reviewer: Piotr Biler (Wrocław)
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37J38 | Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions |
| 34K25 | Asymptotic theory of functional-differential equations |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34M50 | Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain |
| 34M30 | Asymptotics and summation methods for ordinary differential equations in the complex domain |
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