English

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}
}
R2 v1 2026-06-28T23:20:02.760Z