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.
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This work was supported by the National Natural Science Foundation of China (grant No. 11971475) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (grant No. KYCX21_2134).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 209, pp. 465–474 https://doi.org/10.4213/tmf10096.
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Chai, X., Zhang, Y. & Zhao, S. Application of the \(\bar\partial\)-dressing method to a \((2+1)\)-dimensional equation. Theor Math Phys 209, 1717–1725 (2021). https://doi.org/10.1134/S0040577921120059
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DOI: https://doi.org/10.1134/S0040577921120059