Geodesic
Bilinear approach to the~supersymmetric Gardner equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 2, pp. 244-253

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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},
     publisher = {mathdoc},
     volume = {188},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_2_a2/}
}
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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/