Geodesic
Application of the~$\bar\partial$-dressing method to a~$(2+1)$-dimensional equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 465-474

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A remarkable method for investigating solutions of nonlinear soliton equation is the $\bar\partial$-dressing method. Although there are other methods that can also be used for that aim, the $\bar\partial$-dressing method is the most transparent and leads directly to the final results. The $(2+1)$-dimensional Sawada–Kotera equation is studied by analyzing the eigenfunction and the Green's function of its Lax representation as well as by the inverse spectral transformation, yielding a new $\bar\partial$ problem. The solution is constructed based on solving the $\bar\partial$-problem by choosing a proper spectral transformation. Furthermore, once the time evolution of the spectral data is determined, we are able to completely obtain a formal solution of the Sawada–Kotera equation.
Keywords: $\bar\partial$-dressing method, Green's function, eigenfunction
Mots-clés : Sawada–Kotera equation, inverse spectral transformation. 
@article{TMF_2021_209_3_a4,
     author = {Xuedong Chai and Yufeng Zhang and Shiyin Zhao},
     title = {Application of the~$\bar\partial$-dressing method to a~$(2+1)$-dimensional equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {465--474},
     publisher = {mathdoc},
     volume = {209},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a4/}
}
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Xuedong Chai; Yufeng Zhang; Shiyin Zhao. Application of the~$\bar\partial$-dressing method to a~$(2+1)$-dimensional equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 465-474. http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a4/