The ∂̄-dressing method for the (2+1)-dimensional Jimbo-Miwa equation
- 14 April 2022
- journal article
- research article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 150 (7), 2879-2887
- https://doi.org/10.1090/proc/15716
Abstract
The (2+1)-dimensional Jimbo-Miwa equation is analyzed by means of the partial derivative-dressing method. By means of the characteristic function and Green's function of the Lax representation, the problem has been transformed into a new partial derivative problem. A solution is constructed based on solving the partial derivative 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
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