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TMF, 2011, Volume 166, Number 3, Pages 366–387 (Mi tmf6617)  

This article is cited in 8 scientific papers (total in 8 papers)

Super quasiperiodic wave solutions and asymptotic analysis for $\mathcal N=1$ supersymmetric $KdV$-type equations

Y. C. Hona, Engui Fanb

a Department of mathematics, City university of Hong Kong, Hongkong SAR, China
b School of mathematical sciences and key laboratory of mathematics for nonlinear science, Fudan university, Shanghai, China

Abstract: Based on a general multidimensional Riemann theta function and the super Hirota bilinear form, we extend the Hirota method to construct explicit super quasiperiodic (multiperiodic) wave solutions of $\mathcal N=1$supersymmetric KdV-type equations in superspace. We show that the supersymmetric KdV equation does not have an $N$-periodic wave solution with arbitrary parameters for $N\ge2$. In addition, an interesting influencing band occurs among the super quasiperiodic waves under the presence of a Grassmann variable. We also observe that the super quasiperiodic waves are symmetric about this band but collapse along with it. We present a limit procedure for analyzing the asymptotic properties of the super quasiperiodic waves and rigorously show that the super periodic wave solutions tend to super soliton solutions under some “small amplitude” limits.

Keywords: supersymmetric KdV-type equation, super Hirota bilinear method, Riemann theta function, super quasiperiodic wave solution, super soliton solution

DOI: https://doi.org/10.4213/tmf6617

Full text: PDF file (838 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 166:3, 317–336

Bibliographic databases:

Document Type: Article
Received: 03.05.2010
Revised: 19.07.2010

Citation: Y. C. Hon, Engui Fan, “Super quasiperiodic wave solutions and asymptotic analysis for $\mathcal N=1$ supersymmetric $KdV$-type equations”, TMF, 166:3 (2011), 366–387; Theoret. and Math. Phys., 166:3 (2011), 317–336

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gao X.N., Lou S.Y., “Bosonization of supersymmetric KdV equation”, Phys. Lett. B, 707:1 (2012), 209–215  crossref  mathscinet  adsnasa  isi  elib  scopus
    2. Gao X.N., Lou S.Y., Tang X.Ya., “Bosonization, Singularity Analysis, Nonlocal Symmetry Reductions and Exact Solutions of Supersymmetric KdV Equation”, J. High Energy Phys., 2013, no. 5, 029  crossref  mathscinet  zmath  isi  scopus
    3. Xue L.-L., Levi D., Liu Q.P., “Supersymmetric KdV Equation: Darboux Transformation and Discrete Systems”, J. Phys. A-Math. Theor., 46:50 (2013), 502001  crossref  mathscinet  zmath  isi  scopus
    4. Tian Shou-Fu M.P.-L., “On the Quasi-Periodic Wave Solutions and Asymptotic Analysis To a (3+1)-Dimensional Generalized Kadomtsev-Petviashvili Equation”, Commun. Theor. Phys., 62:2 (2014), 245–258  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Zhao Zh., Han B., “Quasiperiodic wave solutions of a (2 + 1)-dimensional generalized breaking soliton equation via bilinear Bäcklund transformation”, Eur. Phys. J. Plus, 131:5 (2016), 128  crossref  mathscinet  isi  elib  scopus
    6. Wang Q., “Constructing Quasi-Periodic Wave Solutions of Differential-Difference Equation by Hirota Bilinear Method”, Z. Naturfors. Sect. A-J. Phys. Sci., 71:12 (2016), 1159–1165  crossref  isi  scopus
    7. Zhao Zh., Chen Y., Han B., “On Periodic Wave Solutions of the KdV6 Equation Via Bilinear Backlund Transformation”, Optik, 140 (2017), 10–17  crossref  isi  scopus
    8. Mao H., Liu Q.P., “Backlund-Darboux Transformations and Discretizations of N=2 a =-2 Supersymmetric KdV Equation”, Phys. Lett. A, 382:5 (2018), 253–258  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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