A kind of explicit quasi-periodic solution and its limit for the Toda lattice equation. (English) Zbl 1151.82320
Summary: Based on the Riemann theta function, the Hirota bilinear method is extended to directly construct a kind of explicit quasi-periodic solution of the Toda lattice equation. The asymptotic property of the quasi-periodic solution is analyzed in detail. It is of interest to see that the well-known soliton solution can be obtained as a limit of the quasi-periodic solution.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 35Q51 | Soliton equations |
References:
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