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arXiv · 1411.0476

Integrable Discretization of Soliton Equations via Bilinear Method and Bäcklund Transformation

Yingnan Zhang·Xiangke Chang·Juan Hu·Xingbiao Hu·Hon-Wah Tam
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Abstract

In this paper, we present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota's bilinear method. This approach is mainly based on the compatibility between an integrable system and its Bäcklund transformation. We apply this procedure to several equations, including the extended Korteweg-de-Vries (KdV) equation, the extended Kadomtsev-Petviashvili (KP) equation, the extended Boussinesq equation, the extended Sawada-Kotera (SK) equation and the extended Ito equation, and obtain their associated semi-discrete analogues. In the continuum limit, these differential-difference systems converge to their corresponding smooth equations. For these new integrable systems, their Bäcklund transformations and Lax pairs are derived

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Yingnan Zhang, Xiangke Chang, Juan Hu, Xingbiao Hu, Hon-Wah Tam. 2014-11-03. Integrable Discretization of Soliton Equations via Bilinear Method and Bäcklund Transformation. https://arxiv.org/abs/1411.0476

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