Third version of the dressing method
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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.
KeywordsRiccati Equation Spectral Problem Volterra Model Toda Chain Periodic Closure
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- 10.L. D. Landau, and E. M. Lifshitz,Course of Theoretical Physics [in Russian], Vol. 3,Quantum Mechanics: Nonrelativistic Theory, Nauka, Moscow (1989); English transl. prev. ed., Oxford Univ. Press, Oxford (1975).Google Scholar