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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 128, Number 1, Pages 43–55
DOI: https://doi.org/10.4213/tmf481
(Mi tmf481)
 

This article is cited in 41 scientific papers (total in 41 papers)

Pfaffianization of the Davey–Stewartson Equations

C. R. Gilson, J. C. Nimmo

University of Glasgow
References:
Abstract: We use the bilinear method from soliton theory to produce a Pfaffian version of the Davey–Stewartson equations. The solutions of this new system of equations are Pfaffians.
English version:
Theoretical and Mathematical Physics, 2001, Volume 128, Issue 1, Pages 870–882
DOI: https://doi.org/10.1023/A:1010446015588
Bibliographic databases:
Language: Russian
Citation: C. R. Gilson, J. C. Nimmo, “Pfaffianization of the Davey–Stewartson Equations”, TMF, 128:1 (2001), 43–55; Theoret. and Math. Phys., 128:1 (2001), 870–882
Citation in format AMSBIB
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\paper Pfaffianization of the Davey--Stewartson Equations
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\transl
\jour Theoret. and Math. Phys.
\yr 2001
\vol 128
\issue 1
\pages 870--882
\crossref{https://doi.org/10.1023/A:1010446015588}
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Linking options:
  • https://www.mathnet.ru/eng/tmf481
  • https://doi.org/10.4213/tmf481
  • https://www.mathnet.ru/eng/tmf/v128/i1/p43
  • This publication is cited in the following 41 articles:
    1. Shen B.-J., Yu G.-F., “Matrix Integral Solutions to the Discrete and Coupled Leznov Lattice Equations”, J. Math. Anal. Appl., 500:2 (2021), 125167  crossref  mathscinet  isi  scopus
    2. Zhang Y., Xu Yu., Ma K., “New Type of a Generalized Variable-Coefficient Kadomtsev-Petviashvili Equation With Self-Consistent Sources and Its Grammian-Type Solutions”, Commun. Nonlinear Sci. Numer. Simul., 37 (2016), 77–89  crossref  mathscinet  adsnasa  isi  scopus  scopus
    3. He Y., Hu X.-B., Tam H.-W., Zhang Y.-N., “a New Method To Generate Non-Autonomous Discrete Integrable Systems Via Convergence Acceleration Algorithms”, Eur. J. Appl. Math., 27:2 (2016), 194–212  crossref  mathscinet  zmath  isi  scopus  scopus
    4. V. G. Marikhin, “Three-dimensional lattice of Bäcklund transformations of integrable cases of the Davey–Stewartson system”, Theoret. and Math. Phys., 189:3 (2016), 1718–1725  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. Li Ch.-X. Lafortune S. Shen Sh.-F., “A semi-discrete Kadomtsev-Petviashvili equation and its coupled integrable system”, J. Math. Phys., 57:5 (2016), 053503  crossref  mathscinet  zmath  isi  scopus
    6. Nimmo J.J.C. Zhao J., “Determinant and Pfaffian Solutions of Soliton Equations”, Phys. Scr., 89:3 (2014), 038005  crossref  adsnasa  isi  scopus  scopus
    7. Meng X.-H., Xu X.-G., “Pfaffianization of a (3+1)-Dimensional Generalized Kadomtsev-Petviashvili Equation”, Appl. Math. Lett., 26:6 (2013), 612–616  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Ma W.-X., Xia T., “Pfaffianized Systems for a Generalized Kadomtsev-Petviashvili Equation”, Phys. Scr., 87:5 (2013), 055003  crossref  zmath  adsnasa  isi  scopus  scopus
    9. Fan E.-G., Chow K.-W., Li J.-H., “On Doubly Periodic Standing Wave Solutions of the Coupled Higgs Field Equation”, Stud Appl Math, 128:1 (2012), 86–105  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Meng G.-Q., Gao Y.-T., Yu X., Qin Y., “Multi-Soliton and Pfaffian Solutions of a (2+1)-Dimensional Nonlinear Evolution Equation via the Jaulent-Miodek Hierarchy”, Appl. Math. Comput., 218:22 (2012), 10791–10802  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Sun Y.-P., Tam H.-W., “On the general variable-coefficient KP equation with self-consistent sources”, J Math Phys, 52:7 (2011), 073511  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    12. Meng X.-H., Tian B., Zhang H.-Q., “Pfaffianization of the generalized variable-coefficient Kadomtsev-Petviashvili equation”, Applied Mathematics and Computation, 217:4 (2010), 1300–1305  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Li, CX, “COMMUTATIVITY OF PFAFFIANIZATION AND BACKLUND TRANSFORMATIONS: THE LEZNOV LATTICE”, Journal of Nonlinear Mathematical Physics, 16:2 (2009), 169  crossref  mathscinet  adsnasa  isi  scopus  scopus
    14. Zhao, JX, “Commutativity of Pfaffianization and Backlund Transformations: Two Differential-Difference Systems”, Journal of the Physical Society of Japan, 78:6 (2009), 064005  crossref  mathscinet  adsnasa  isi  scopus  scopus
    15. Sun, YP, “On the non-isospectral Kadomtsev-Petviashvili equation with self-consistent sources”, Nonlinear Analysis-Theory Methods & Applications, 70:4 (2009), 1610  crossref  mathscinet  zmath  isi  scopus  scopus
    16. Yuan-Yuan Zhang, Ying Zheng, Hong-Qing Zhang, “Pfaffianization of the variable-coefficient KP equation”, Chaos, Solitons & Fractals, 39:3 (2009), 1000  crossref
    17. Sun, YP, “Grammian solutions and Pfaffianization of the non-isospectral modified Kadomtsev-Petviashvili equation”, Physics Letters A, 372:24 (2008), 4412  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    18. Sun, YP, “Grammian solutions and Pfaffianization of a non-isospectral and variable-coefficient Kadomtsev-Petviashvili equation”, Journal of Mathematical Analysis and Applications, 343:2 (2008), 810  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    19. Wang, HY, “On the Pfaffianized-KP equation with self-consistent sources”, Journal of Mathematical Analysis and Applications, 338:1 (2008), 82  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    20. Hu, J, “Source generation of the Davey-Stewartson equation”, Journal of Mathematical Physics, 49:1 (2008), 013506  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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