The application of the ∂¯-dressing method to the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

Huanhuan Lu; Yufeng Zhang

doi:10.1216/rmj.2021.51.2137

Abstract

Starting from a Lax pair, we study the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) equation by means of the $\bar\partial$ -dressing method, which can be employed to formulate scattering equations and to solve the inverse scattering problem. Based on that, the solutions of the DJKM equation can be further worked out.

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Huanhuan Lu. Yufeng Zhang. "The application of the $\bar\partial$ -dressing method to the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation." Rocky Mountain J. Math. 51 (6) 2137 - 2145, December 2021. https://doi.org/10.1216/rmj.2021.51.2137

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Received: 25 January 2021; Revised: 14 March 2021; Accepted: 20 March 2021; Published: December 2021

First available in Project Euclid: 22 March 2022

MathSciNet: MR4397669

zbMATH: 1487.35009

Digital Object Identifier: 10.1216/rmj.2021.51.2137

Subjects:

Primary: 35Axx

Keywords: (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation , ∂¯-dressing method , Eigenfunctions , Green functions

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