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This article is cited in 8 scientific papers (total in 8 papers)
Application of the $\bar\partial$-dressing method to a $(2+1)$-dimensional equation
Xuedong Chaia, Yufeng Zhanga, Shiyin Zhaoab a School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China
b College of Mathematics, Suqian University, Suqian, Jiangsu, China
Abstract:
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, Sawada–Kotera equation, inverse spectral transformation.
Received: 17.03.2021 Revised: 30.04.2021
Citation:
Xuedong Chai, Yufeng Zhang, Shiyin Zhao, “Application of the $\bar\partial$-dressing method to a $(2+1)$-dimensional equation”, TMF, 209:3 (2021), 465–474; Theoret. and Math. Phys., 209:3 (2021), 1717–1725
Linking options:
https://www.mathnet.ru/eng/tmf10096https://doi.org/10.4213/tmf10096 https://www.mathnet.ru/eng/tmf/v209/i3/p465
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