Li, Min; Liu, Chang-Jing Applications of Bell-polynomial scheme in constructing the conversation laws of the nonlinear evolution equations admitting two-field bilinear forms. (English) Zbl 1394.35422 Int. J. Nonlinear Sci. 21, No. 2, 98-105 (2016). Summary: The Bell-polynomial scheme is applied to obtain the infinite conservation laws for the nonlinear evolution equations (NLEEs) admitting two-field bilinear forms. Bell-polynomial scheme has been used to obtain certain bilinear Bäcklund transformations (BTs), Lax pairs and infinite conservation laws for the NLEEs with one-field bilinear forms. Based on the two-field bilinear forms and four-field bilinear BTs in the binary-Bell-polynominal form, the infinite conversation laws for a variable-coefficient modified Korteweg-de Vries equation arising in fluid and plasma physics as well as the Boussinesq-Burgers equations for the shallow water waves are construed systematically. Such procedure can be applied to other NLEEs admitting two-field bilinear forms. MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 33C80 Connections of hypergeometric functions with groups and algebras, and related topics 35A30 Geometric theory, characteristics, transformations in context of PDEs PDF BibTeX XML Cite \textit{M. Li} and \textit{C.-J. Liu}, Int. J. Nonlinear Sci. 21, No. 2, 98--105 (2016; Zbl 1394.35422)