Geodesic
On the infinite-dimensional noncommutative Lie–Bäcklund algebra associated with the equations of one-dimensional gas dynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 56 (1983) no. 3, pp. 368-386 
M. B. Sheftel. On the infinite-dimensional noncommutative Lie–Bäcklund algebra associated with the equations of one-dimensional gas dynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 56 (1983) no. 3, pp. 368-386. http://geodesic.mathdoc.fr/item/TMF_1983_56_3_a4/
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     title = {On the infinite-dimensional noncommutative {Lie{\textendash}B\"acklund} algebra associated with the equations of one-dimensional gas dynamics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {56},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1983_56_3_a4/}
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A study is made of the infinite-dimensional noncommutative Lie–Bäcklund algebra associated with the equations of one-dimensional plane isentropic flow of a gas and with the infinite set of systems of evolution equations associated with them. Infinite series of invariant solutions and conservation laws and $L-A$ pairs for all these equations are obtained. A new operator method for finding invariant solutions is proposed.

[1] Ibragimov N. Kh., Anderson R. L., DAN SSSR, 227:3 (1976), 539–542 | MR | Zbl

[2] Ibragimov N. Kh., DAN SSSR, 230:1 (1976), 26–29 | MR | Zbl

[3] Ibragimov N. Kh., Matem. sb., 109 (151):2 (6) (1979), 229–253 | MR | Zbl

[4] Ibragimov N. H., Anderson R. L., J. Math. Anal. Appl., 59:1 (1977), 145–162 | DOI | MR | Zbl

[5] Ibragimov N. Kh., Shabat A. B., DAN SSSR, 244:1 (1979), 57–61 | MR | Zbl

[6] Zhiber A. V., Shabat A. B., DAN SSSR, 247:5 (1979), 1103–1107 | MR

[7] Ibragimov N. Kh., Shabat A. B., Funkts. analiz i ego prilozh., 14:1 (1980), 25–36 | MR | Zbl

[8] Ibragimov N. Kh., Shabat A. B., Funkts. analiz i ego prilozh., 14:4 (1980), 79–80 | MR | Zbl

[9] Ibragimov N. H., C. R. Acad. Scient. Paris, Serie 1, 293 (1981), 657–660 | MR | Zbl

[10] Zakharov V. E., Faddeev L. D., Funkts. analiz i ego prilozh., 5:4 (1971), 18–27 | MR | Zbl

[11] Sheftel M. B., Vestn. LGU, 1982, no. 7, 37–41 | MR | Zbl

[12] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1978 | MR | Zbl

[13] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov: Metod obratnoi zadachi, ed. S. P. Novikov, Nauka, M., 1980 | MR

[14] Yanenko N. N., “Teoriya sovmestnosti i metody integrirovaniya sistem nelineinykh uravnenii v chastnykh proizvodnykh”, Tr. IV Vsesoyuznogo matem. s'ezda, 2, Nauka, L., 1964, 613–621