### The ∂̄-dressing method for the (2+1)-dimensional Jimbo-Miwa equation

Xuedong Chai, Yufeng Zhang, Yong Chen, Shiyin Zhao
Published: 14 April 2022

Abstract: The (2+1)-dimensional Jimbo-Miwa equation is analyzed by means of the $\bar {{\partial }}$-dressing method. By means of the characteristic function and Green’s function of the Lax representation, the problem has been transformed into a new $\bar {{\partial }}$ problem. A solution is constructed based on solving the $\bar {{\partial }}$ problem with the help of Cauchy-Green formula and choosing the proper spectral transformation. Furthermore, we can obtain the solution formally of the Jimbo-Miwa equation when the time evolution of the spectral data is determined.
Keywords: dressing method / math/mathml / inline / Miwa / Jimbo / equation / content type / formula content

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