Darboux transformation and multi-soliton solutions of the discrete sine-Gordon equation. (English) Zbl 1481.39016
Summary: We study the discrete Darboux transformation and construct multi-soliton solutions in terms of the ratio of determinants for the integrable discrete sine-Gordon equation. We also calculate explicit expressions of single-, double-, triple-, and quadruple-soliton solutions as well as single- and double-breather solutions of the discrete sine-Gordon equation. The dynamical features of discrete kinks and breathers are also illustrated.
MSC:
| 39A36 | Integrable difference and lattice equations; integrability tests |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K60 | Lattice dynamics; integrable lattice equations |
| 35Q51 | Soliton equations |
