Keywords: dressing chain, Dym equation
@article{TMF_2006_149_1_a2,
author = {V. E. Adler and A. B. Shabat},
title = {Dressing chain for the~acoustic spectral problem},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {32--46},
year = {2006},
volume = {149},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2006_149_1_a2/}
}
V. E. Adler; A. B. Shabat. Dressing chain for the acoustic spectral problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 1, pp. 32-46. http://geodesic.mathdoc.fr/item/TMF_2006_149_1_a2/
[1] M. Kruskal, “Nonlinear wave equations”, Dynamical systems, theory and applications, Lect. Notes in Phys., 38, ed. J. Moser, Springer, Heidelberg, 1975, 310–354 | DOI | MR | Zbl
[2] B. Fuchssteiner, A. S. Fokas, Physica D, 4 (1981), 47–66 ; R. Camassa, D. D. Holm, Phys. Rev. Lett., 71 (1993), 1661–1664 | DOI | MR | Zbl | DOI | MR | Zbl
[3] M. G. Krein, DAN SSSR, 82 (1952), 669–672 | MR | Zbl
[4] F. Calogero, A. Degasperis, Spectral transforms and solitons, North-Holland, Amsterdam, 1982 | MR | Zbl
[5] R. Beals, D. Sattinger, J. Szmigielski, Adv. Math., 140 (1998), 190–206 | DOI | MR | Zbl
[6] A. Constantin, Proc. Roy. Soc. Lond. A, 457 (2001), 953–970 | DOI | MR | Zbl
[7] L. A. Dmitrieva, Phys. Lett. A, 182:1 (1993), 65–70 ; J. Phys. A, 26 (1993), 6005–6020 ; A. Constantin, H. P. McKean, Commun. Pure Appl. Math., 52 (1999), 949–982 ; В. С. Новиков, Письма в ЖЭТФ, 72:3 (2000), 223–228; M. S. Alber, Yu. N. Fedorov, Inverse Problems, 17 (2001), 1017–1042 ; M. S. Alber, R. Camassa, Yu. N. Fedorov, D. D. Holm, J. E. Marsden, Commun. Math. Phys., 221 (2001), 197–227 ; R. Camassa, A. I. Zenchuk, Phys. Lett. A, 281 (2001), 26–33 | DOI | MR | DOI | MR | Zbl | 3.0.CO;2-D class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl
[8] J. Schiff, Physica D, 121 (1998), 24–43 ; A. N. W. Hone, J. Phys. A, 32 (1999), L307–L314 ; R. Ivanov, Phys. Lett. A, 345 (2005), 112–118 ; nlin.SI/0507005 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl
[9] M. M. Crum, Quart. J. Math. Oxford 2, 6 (1995), 121–127 | DOI | MR
[10] Dzh. L. Lem, Vvedenie v teoriyu solitonov, Mir, M., 1984 | MR
[11] A. B. Shabat, Inverse Problems, 8 (1992), 303–308 ; А. П. Веселов, А. Б. Шабат, Функц. анализ и его прилож., 27:2 (1993), 1–21 | DOI | MR | Zbl | MR | Zbl
[12] A. B. Shabat, R. I. Yamilov, Algebra i analiz, 2:2 (1990), 183–208 | MR | Zbl
[13] R. H. Heredero, J. Nonlinear Math. Phys., 12:4 (2005), 567–585 | DOI | MR | Zbl
[14] R. I. Yamilov, TMF, 85:3 (1990), 368–375 | MR | Zbl
[15] R. Beals, M. Rabelo, K. Tenenblat, Stud. Appl. Math., 81 (1989), 125–151 ; T. Schäfer, C. E. Wayne, Physica D, 196 (2004), 90–105 | DOI | MR | Zbl | DOI | MR | Zbl
[16] G. Falqui, On a Camassa–Holm type equation with two dependent variables, ; H. Aratyn, J. F. Gomes, A. H. Zimerman, J. Phys. A, 39 (2006), 1099–1114 nlin.SI/0505059 | MR | DOI | MR | Zbl
[17] A. Degasperis, M. Procesi, “Asymptotic integrability”, Symmetry and perturbation theory, Proc. 2nd Int. Workshop (Rome, Italy, December 16–22, 1998), eds. A. Degasperis, G. Gaeta, World Scientific, Singapore, 1999, 23–37 ; А. Дегасперис, Д. Д. Холм, А. Н И. Хон, ТМФ, 133:2 (2002), 170–183 | MR | Zbl | DOI | MR
[18] V. E. Adler, V. G. Marikhin, A. B Shabat, TMF, 129:2 (2001), 163–183 | DOI | MR | Zbl
[19] V. G. Dubrovsky, B. G. Konopelchenko, J. Phys. A, 27:13 (1994), 4619–4628 ; L. A. Dmitrieva, M. A. Khlabystova, Phys. Lett. A, 237:6 (1998), 369–380 | DOI | MR | Zbl | DOI | MR | Zbl