Geodesic
Reduction of the dressing chain of the Schr\"odinger operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 3, pp. 424-432

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We reduce the problem of constructing real finite-gap solutions of the focusing modified Korteweg–de Vries equation to the dressing chain of the Schrödinger operator. We show that the Schrödinger operator spectral curve corresponding to such a solution is real. We give some restrictions on the initial data for the chain that lead to such solutions. We also consider a soliton reduction. We obtain compact representations for the multisoliton and breather solutions of the modified Korteweg–de Vries equationentations can be useful in developing the perturbation theory for various applied problems. 
@article{TMF_2000_123_3_a4,
     author = {M. Yu. Kulikov and V. S. Novikov},
     title = {Reduction of the dressing chain of the {Schr\"odinger} operator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {424--432},
     publisher = {mathdoc},
     volume = {123},
     number = {3},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a4/}
}
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M. Yu. Kulikov; V. S. Novikov. Reduction of the dressing chain of the Schr\"odinger operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 3, pp. 424-432. http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a4/