Darboux transformation and soliton solutions of the semi-discrete massive Thirring model. (English) Zbl 1477.81062
Summary: A one-fold Darboux transformation between solutions of the semi-discrete massive Thirring model is derived using the Lax pair and the dressing method. This transformation is used to find the exact expressions for soliton solutions on zero and nonzero backgrounds. It is shown that the discrete solitons have the same properties as their continuous counterparts.
MSC:
| 81T10 | Model quantum field theories |
| 81V74 | Fermionic systems in quantum theory |
| 39A12 | Discrete version of topics in analysis |
| 39A36 | Integrable difference and lattice equations; integrability tests |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
| 35C08 | Soliton solutions |
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