Geodesic
Miura-type transformations of nonlinear partial differential equations integrable by the $\bar\partial$-problem method
Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 1, pp. 47-54 
A. I. Zenchuk. Miura-type transformations of nonlinear partial differential equations integrable by the $\bar\partial$-problem method. Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 1, pp. 47-54. http://geodesic.mathdoc.fr/item/TMF_1999_119_1_a3/
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     author = {A. I. Zenchuk},
     title = {Miura-type transformations of nonlinear partial differential equations integrable by the $\bar\partial$-problem method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {47--54},
     year = {1999},
     volume = {119},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_119_1_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new method is suggested for constructing Miura-type transformations for systems of nonlinear equations of mathematical physics integrable by the $\bar\partial$-problem method using a generalized normalization function in the $\bar\partial$-problem. Examples of these transformations for the Kadomtsev–Petviashvili equation are considered.

[1] V. E. Zakharov, A. B. Shabat, Funkts. analiz i ego prilozh., 8:3 (1974), 43 | MR | Zbl

[2] V. E. Zakharov, S. V. Manakov, Funkts. analiz i ego prilozh., 19:2 (1985), 11 | MR | Zbl

[3] L. V. Bogdanov, S. V. Manakov, J. Phys. A, 21 (1988), L537 | DOI | MR | Zbl

[4] A. I. Zenchuk, S. V. Manakov, TMF, 105:3 (1995), 371 | MR | Zbl