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TMF, 2012, Volume 170, Number 3, Pages 350–380 (Mi tmf6772)  

This article is cited in 14 scientific papers (total in 14 papers)

Super Riemann theta function periodic wave solutions and rational characteristics for a supersymmetric KdV–Burgers equation

Shou-fu Tianab, Hong-qing Zhangb

a Department of Mathematics, University of British Columbia, Vancouver, Canada
b School of Mathematical Sciences, Dalian University of Technology, Dalian, China

Abstract: Using a multidimensional super Riemann theta function, we propose two key theorems for explicitly constructing multiperiodic super Riemann theta function periodic wave solutions of supersymmetric equations in the superspace $\mathbb{R}_{\Lambda}^{N+1,M}$, which is a lucid and direct generalization of the super-Hirota–Riemann method. Once a supersymmetric equation is written in a bilinear form, its super Riemann theta function periodic wave solutions can be directly obtained by using our two theorems. As an application, we present a supersymmetric Korteweg–de Vries–Burgers equation. We study the limit procedure in detail and rigorously establish the asymptotic behavior of the multiperiodic waves and the relations between periodic wave solutions and soliton solutions. Moreover, we find that in contrast to the purely bosonic case, an interesting phenomenon occurs among the super Riemann theta function periodic waves in the presence of the Grassmann variable. The super Riemann theta function periodic waves are symmetric about the band but collapse along with the band. Furthermore, the results can be extended to the case $N>2$; here, we only consider an existence condition for an $N$-periodic wave solution of a general supersymmetric equation.

Keywords: supersymmetric Korteweg–de Vries–Burgers equation, super-Hirota bilinear form, Riemann theta function, super Riemann theta function periodic wave solution, solitary wave solution

DOI: https://doi.org/10.4213/tmf6772

Full text: PDF file (1367 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 170:3, 287–314

Bibliographic databases:

Document Type: Article
Received: 27.04.2011

Citation: Shou-fu Tian, Hong-qing Zhang, “Super Riemann theta function periodic wave solutions and rational characteristics for a supersymmetric KdV–Burgers equation”, TMF, 170:3 (2012), 350–380; Theoret. and Math. Phys., 170:3 (2012), 287–314

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. Sh.-F. Tian, B. Lu, Ya. Feng, H.-Q. Zhang, Ch. Yang, “Hyperelliptic function solutions with finite genus $\mathscr G$ of coupled nonlinear differential equations”, J. Nonlinear Math. Phys., 20:2 (2013), 245–259  crossref  mathscinet  isi  elib  scopus
    2. Sh.-F. Tian, H.-Q. Zhang, “Riemann theta functions periodic wave solutions and rational characteristics for the $(1+1)$-dimensional and $(2+1)$-dimensional Ito equation”, Chaos Solitons Fractals, 47 (2013), 27–41  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. P.-L. Ma, Sh.-F. Tian, “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
    4. Sh.-F. Tian, H.-Q. Zhang, “On the integrability of a generalized variable-coefficient forced Korteweg-de Vries equation in fluids”, Stud. Appl. Math., 132:3 (2014), 212–246  crossref  mathscinet  zmath  isi  scopus
    5. Sh. Tian, Yu. Zhang, B. Feng, H. Zhang, “On the Lie algebras, generalized symmetries and Darboux transformations of the fifth-order evolution equations in shallow water”, Chin. Ann. Math. Ser. B, 36:4 (2015), 543–560  crossref  mathscinet  zmath  isi  scopus
    6. S. Demiray, F. Tascan, “Quasi-periodic solutions of $(3+1)$ generalized BKP equation by using Riemann theta functions”, Appl. Math. Comput., 273 (2016), 131–141  crossref  mathscinet  isi  scopus
    7. Ch.-Ya. Qin, Sh.-F. Tian, X.-B. Wang, T.-T. Zhang, “Quasi-periodic wave solutions and asymptotic properties for a fifth-order Korteweg-de Vries type equation”, Mod. Phys. Lett. B, 30:18 (2016), 1650223  crossref  mathscinet  isi  scopus
    8. X.-W. Yan, Sh.-F. Tian, M.-J. Dong, L. Zou, “Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev-Petviashvili equation”, Mod. Phys. Lett. B, 31:36 (2017), 1750350  crossref  mathscinet  isi
    9. L. Zou, Sh.-F. Tian, X.-B. Wang, T.-T. Zhang, “Lie symmetry analysis and different types of solutions to a generalized bidirectional sixth-order Sawada-Kotera equation”, Chin. J. Phys., 55:6 (2017), 2236–2248  crossref  mathscinet  isi  scopus
    10. L. Zou, Z.-B. Yu, Sh.-F. Tian, L.-L. Feng, J. Li, “Lump solutions with interaction phenomena in the $(2+1)$-dimensional Ito equation”, Mod. Phys. Lett. B, 32:7 (2018), 1850104  crossref  mathscinet  isi  scopus
    11. Ch.-Ya. Qin, Sh.-F. Tian, X.-B. Wang, T.-T. Zhang, J. Li, “Rogue waves, bright-dark solitons and traveling wave solutions of the $(3+1)$-dimensional generalized Kadomtsev-Petviashvili equation”, Comput. Math. Appl., 75:12 (2018), 4221–4231  crossref  mathscinet  isi  scopus
    12. J.-J. Mao, Sh.-F. Tian, L. Zou, T.-T. Zhang, “Optical solitons, complexitons, Gaussian soliton and power series solutions of a generalized Hirota equation”, Mod. Phys. Lett. B, 32:14 (2018), 1850143  crossref  mathscinet  isi  scopus
    13. X.-W. Yan, Sh.-F. Tian, M.-J. Dong, L. Zhou, T.-T. Zhang, “Characteristics of solitary wave, homoclinic breather wave and rogue wave solutions in a $(2+1)$-dimensional generalized breaking soliton equation”, Comput. Math. Appl., 76:1 (2018), 179–186  crossref  mathscinet  isi  scopus
    14. Guo D., Tian Sh.-F., “Stability Analysis, Soliton Waves, Rogue Waves and Interaction Phenomena For the (3+1)-Dimensional Generalized Kadomtsev-Petviashvili Equation”, Mod. Phys. Lett. B, 32:28 (2018), 1850345  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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