Finding of $N$-soliton solutions of multidimensional nonlinear equations by means of Hirota's method
Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 1, pp. 69-76 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An infinite set of multidimensional nonlinear equations is proposed for which Hirota's method can be used to construct one-soliton and two-soliton solutions. Some of these equations have $N$-soliton solutions for any $N$. For each of the proposed equations, a family of rational solutions is constructed. It is shown that in the case of three independent variables, this family contains two-dimensional solitons.
@article{TMF_1979_41_1_a7,
     author = {B. I. Shubov},
     title = {Finding of $N$-soliton solutions of multidimensional nonlinear equations by means of {Hirota's} method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {69--76},
     year = {1979},
     volume = {41},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_41_1_a7/}
}
TY  - JOUR
AU  - B. I. Shubov
TI  - Finding of $N$-soliton solutions of multidimensional nonlinear equations by means of Hirota's method
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1979
SP  - 69
EP  - 76
VL  - 41
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1979_41_1_a7/
LA  - ru
ID  - TMF_1979_41_1_a7
ER  - 
%0 Journal Article
%A B. I. Shubov
%T Finding of $N$-soliton solutions of multidimensional nonlinear equations by means of Hirota's method
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1979
%P 69-76
%V 41
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1979_41_1_a7/
%G ru
%F TMF_1979_41_1_a7
B. I. Shubov. Finding of $N$-soliton solutions of multidimensional nonlinear equations by means of Hirota's method. Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 1, pp. 69-76. http://geodesic.mathdoc.fr/item/TMF_1979_41_1_a7/

[1] R. Hirota, Phys. Rev. Lett., 27 (1971), 1192 | DOI | Zbl

[2] K. Sawada, T. Kotera, Progr. Theor. Phys., 51 (1974), 1355 | DOI | MR | Zbl

[3] R. Hirota, J. Math. Phys., 14 (1973), 810 | DOI | MR | Zbl

[4] R. Hirota, J. Satsuma, J. Phys. Soc. Japan, 40 (1976), 611 | DOI | MR | Zbl

[5] J. Satsuma, J. Phys. Soc. Japan, 40 (1976), 286 | DOI | MR | Zbl

[6] R. Hirota, J. Satsuma, Suppl. Progr. Theor. Phys., 59 (1976) | DOI | MR

[7] P. J. Caudrey, R. K. Dodd, J. D. Gibbon, Proc. Roy. Soc. London, 351 (1976), 407 | DOI | MR | Zbl

[8] R. Hirota, Preprint of Hiroshima Univ., 1977

[9] L. A. Bordag, A. R. Its, V. B. Matveev, S. V. Manakov, V. E. Zakharov, Preprint of Leipzic Univ., 1977 | Zbl

[10] E. Gursa, Kurs matematicheskogo analiza, t. I, ch. 1, GTTI, 1933