Summary
Two applications of the concept of soliton surfaces are discussed. Firstly, soliton surfaces can serve as a territory of unification of four types of solvable nonlinearities: 1) soliton, 2) strings, 3) spins and 4) chiral models. It is conjectured that models 2), 3) and 4) associated with a given soliton system are gauge equivalent to this soliton system. Secondly, an explicit construction of the soliton surface associated with a given soliton solution gives simultaneously the corresponding solutions to models 2), 3) and 4). Using the Hilbert-Riemann problem technique a construction of N-soliton surfaces is described. Examples including new soliton systems are given.
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Research supported in part by Polish Ministry of Science, Higher Education and Technology. Grant M.K.I.7.
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Sym, A. Soliton surfaces. Lett. Nuovo Cimento 36, 307–312 (1983). https://doi.org/10.1007/BF02719461
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DOI: https://doi.org/10.1007/BF02719461