Geodesic
$\bar\partial$-dressing method for a few ($2+1$)-dimensional integrable coupling systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 3, pp. 452-470

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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 $\bar\partial$-dressing method to investigate these integrable coupling systems and obtain some exact solutions by solving the coupled $\bar\partial$-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.
Keywords: $\bar\partial$-dressing method, integrable coupling system, inverse spectral transform method
Mots-clés : exact solution. 
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     author = {Haifeng Wang and Yufeng Zhang},
     title = {$\bar\partial$-dressing method for a few ($2+1$)-dimensional integrable coupling systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {452--470},
     publisher = {mathdoc},
     volume = {208},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a5/}
}
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Haifeng Wang; Yufeng Zhang. $\bar\partial$-dressing method for a few ($2+1$)-dimensional integrable coupling systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 3, pp. 452-470. http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a5/