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arXiv · 2505.01771

Nonlinearization of the KdV-type and mKdV-type bilinear equations

Xin Zhang·Jin Liu·Da-jun Zhang
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Abstract

In this paper, we show a general procedure to nonlinearize bilinear equations by using the Bell polynomials. As applications, we obtain nonlinear forms of some integrable bilinear equations (in the sense having 3-soliton solutions) of the KdV type and mKdV type that were found by Jarmo Hietarinta in 1980s. Examples of non-integrable bilinear equations of the KdV type are also given.

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Xin Zhang, Jin Liu, Da-jun Zhang. 2025-05-03. Nonlinearization of the KdV-type and mKdV-type bilinear equations. https://arxiv.org/abs/2505.01771

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