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Supersymmetric KdV-Sawada-Kotera-Ramani equation and its quasi-periodic wave solutions. (English) Zbl 1235.35242

Summary: In this Letter, we propose a supersymmetric KdV-Sawada-Kotera-Ramani equation. Based on a super-Riemann theta function, we devise a lucid and straightforward way for explicitly constructing a quasi-periodic wave solution of the supersymmetric KdV-Sawada-Kotera-Ramani equation. In addition, a one-soliton solution is obtained as a limiting case of the periodic wave solution under small amplitude. Indeed different from the purely bosonic case, the quasi-periodic wave observed shows that there is an “influencing band” among the waves under the presence of the Grassmann variable. The waves are symmetric about the band but collapse along with the band. Furthermore, the amplitudes of the waves increase as the waves move away from the band.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
81Q60 Supersymmetry and quantum mechanics
14K25 Theta functions and abelian varieties
35C07 Traveling wave solutions
35C08 Soliton solutions
14M15 Grassmannians, Schubert varieties, flag manifolds
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