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Third version of the dressing method. (English. Russian original) Zbl 0987.35133
Theor. Math. Phys. 121, No. 1, 1397-1408 (1999); translation from Teor. Mat. Fiz. 121, No. 1, 165-176 (1999).
Author’s abstract: The two previous versions of the dressing method in soliton theory were elaborated in collaboration with V. E. Zakharov. In our works published in the 1970s, we did not consider discrete equations on a lattice, Painlevé-type equations, and finite-band potentials, and I now make up for this gap. Although the suggested elementary discretization scheme for the linear spectral problem is rather general, the presentation of the material is mainly confined to the framework of the Zakharov-Shabat spectral problem.

##### MSC:
 35Q40 PDEs in connection with quantum mechanics 37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems 39A13 Difference equations, scaling ($$q$$-differences)
##### Keywords:
Zakharov-Shabat spectral problem; dressing method
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##### References:
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