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

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

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English version:
Theoretical and Mathematical Physics, 2011, 166:3, 317–336

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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
\Bibitem{HonFan11} \by Y.~C.~Hon, Engui~Fan \paper Super quasiperiodic wave solutions and asymptotic analysis for $\mathcal N=1$ supersymmetric $\text{KdV}$-type equations \jour TMF \yr 2011 \vol 166 \issue 3 \pages 366--387 \mathnet{http://mi.mathnet.ru/tmf6617} \crossref{https://doi.org/10.4213/tmf6617} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2011TMP...166..317H} \transl \jour Theoret. and Math. Phys. \yr 2011 \vol 166 \issue 3 \pages 317--336 \crossref{https://doi.org/10.1007/s11232-011-0026-x} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000293733500004} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955096386} 

• http://mi.mathnet.ru/eng/tmf6617
• https://doi.org/10.4213/tmf6617
• http://mi.mathnet.ru/eng/tmf/v166/i3/p366

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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
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
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
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
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
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
7. Zhao Zh., Chen Y., Han B., “On Periodic Wave Solutions of the KdV6 Equation Via Bilinear Backlund Transformation”, Optik, 140 (2017), 10–17
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
9. A. Mirza, M. ul Hassan, “Bilinearization and soliton solutions of a supersymmetric multicomponent coupled dispersionless integrable system”, Theoret. and Math. Phys., 201:3 (2019), 1723–1731
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