Nonlinearization of the KdV-type and mKdV-type bilinear equations
Exactly Solvable and Integrable Systems
2025-05-06 v1
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.
Keywords
Cite
@article{arxiv.2505.01771,
title = {Nonlinearization of the KdV-type and mKdV-type bilinear equations},
author = {Xin Zhang and Jin Liu and Da-jun Zhang},
journal= {arXiv preprint arXiv:2505.01771},
year = {2025}
}