Abstract:
Several (2+1)-dimensional integrable coupling systems are derived from two sets of auxiliary linear problems, including the integrable coupling system of a (2+1)-dimensional generalization of the dispersive long-wave system, and a (2+1)-dimensional generalizations of the Burgers equation and the Davey–Stewartson system. We use the ¯∂-dressing method to investigate these integrable coupling systems and obtain some exact solutions by solving the coupled ¯∂-problem that we introduce. The methods and techniques presented in this paper may be good inspiration for dealing with similar problems and the corresponding integrable coupling systems.
\Bibitem{WanZha21}
\by Haifeng~Wang, Yufeng~Zhang
\paper $\bar\partial$-dressing method for a few ($2+1$)-dimensional integrable coupling systems
\jour TMF
\yr 2021
\vol 208
\issue 3
\pages 452--470
\mathnet{http://mi.mathnet.ru/tmf10059}
\crossref{https://doi.org/10.4213/tmf10059}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2021TMP...208.1239W}
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\transl
\jour Theoret. and Math. Phys.
\yr 2021
\vol 208
\issue 3
\pages 1239--1255
\crossref{https://doi.org/10.1134/S0040577921090063}
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Linking options:
https://www.mathnet.ru/eng/tmf10059
https://doi.org/10.4213/tmf10059
https://www.mathnet.ru/eng/tmf/v208/i3/p452
This publication is cited in the following 5 articles:
Haifeng Wang, Yufeng Zhang, Binlu Feng, “A class of extended high-dimensional nonisospectral KdV hierarchies and symmetry”, Zeitschrift für Naturforschung A, 2025
Haifeng Wang, Yufeng Zhang, “Generation of higher-dimensional isospectral-nonisospectral integrable hierarchies associated with a new class of higher-dimensional column-vector loop algebra”, Theoret. and Math. Phys., 219:2 (2024), 722–747
H. Wang, Yu. Zhang, “A new multi-component integrable coupling and its application to isospectral and nonisospectral problems”, Commun. Nonlinear Sci. Numer. Simul., 105 (2022), 106075
X. Chai, Y. Zhang, “The ¯¯¯∂-dressing method for the (2+1)-dimensional Konopelchenko–Dubrovsky equation”, Applied Mathematics Letters, 134 (2022), 108378
Y. Huang, J. Di, Y. Yao, “¯¯¯∂-dressing method for a generalized Hirota equation”, Int. J. Mod. Phys. B, 36:19 (2022)
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