Geodesic
Bilinear approach to the supersymmetric Gardner equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 2, pp. 244-253 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study a supersymmetric version of the Gardner equation (both focusing and defocusing) using the superbilinear formalism. This equation is new and cannot be obtained from the supersymmetric modified Korteweg–de Vries equation with a nonzero boundary condition. We construct supersymmetric solitons and then by passing to the long-wave limit in the focusing case obtain rational nonsingular solutions. We also discuss the supersymmetric version of the defocusing equation and the dynamics of its solutions.
Keywords: supersymmetry, supersymmetric Hirota bilinear formalism
Mots-clés : supersoliton. 
@article{TMF_2016_188_2_a2,
     author = {C. N. Babalic and A. S. Carstea},
     title = {Bilinear approach to the~supersymmetric {Gardner} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {244--253},
     year = {2016},
     volume = {188},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_2_a2/}
}
TY  - JOUR
AU  - C. N. Babalic
AU  - A. S. Carstea
TI  - Bilinear approach to the supersymmetric Gardner equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 244
EP  - 253
VL  - 188
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_188_2_a2/
LA  - ru
ID  - TMF_2016_188_2_a2
ER  - 
%0 Journal Article
%A C. N. Babalic
%A A. S. Carstea
%T Bilinear approach to the supersymmetric Gardner equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 244-253
%V 188
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2016_188_2_a2/
%G ru
%F TMF_2016_188_2_a2
C. N. Babalic; A. S. Carstea. Bilinear approach to the supersymmetric Gardner equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 2, pp. 244-253. http://geodesic.mathdoc.fr/item/TMF_2016_188_2_a2/

[1] A. S. Carstea, Nonlinearity, 13:5 (2000), 1645–1656 | DOI | MR | Zbl

[2] A. S. Carstea, A. Ramani, B. Grammaticos, Nonlinearity, 14 (2001), 1419–1424 | DOI | MR

[3] B. Grammaticos, A. Ramani, A. S. Carstea, J. Phys. A: Math. Gen., 34:23 (2001), 4881–4886 | DOI | MR | Zbl

[4] A. S. Carstea, A. Ramani, B. Grammaticos, Chaos Solitons Fractals, 14:1 (2002), 155–158 | DOI | MR | Zbl

[5] A. S. Carstea, D. Grecu, A. Visinescu, Europhys. Lett., 67:4 (2004), 531–537 | DOI | MR

[6] Q. P. Liu, X.-B. Hu, M.-X. Zhang, Nonlinearity, 18:4 (2005), 1597–1604 | DOI | MR

[7] Q. P. Liu, X.-B. Hu, J. Phys. A: Math. Gen., 38:28 (2005), 6371–6378 | DOI | MR | Zbl

[8] Q. P. Liu, X.-X. Yang, Phys. Lett. A, 351:3 (2006), 131–135 | DOI | MR | Zbl

[9] E. Fan, Stud. Appl. Math., 127:3 (2011), 284–301 | DOI | MR | Zbl

[10] M.-X. Zhang, Q. P. Liu, Y.-L. Shen, K. Wu, Sci. China A: Math., 52:9 (2009), 1973–1981 | DOI | MR | Zbl

[11] A. S. Carstea, J. Phys. A: Math. Theor., 48:28 (2015), 285201, 13 pp. | DOI | MR | Zbl

[12] M. J. Ablowitz, J. Satsuma, J. Math. Phys., 19:10 (1978), 2180–2186 | DOI | MR | Zbl

[13] Y. Chen, P. L.-F. Liu, Wave Motion, 24:2 (1996), 169–184 | DOI | MR | Zbl