an:06932892
Zbl 1394.35422
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
EN
Int. J. Nonlinear Sci. 21, No. 2, 98-105 (2016).
00360812
2016
j
35Q53 37K35 33C80 35A30
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 B??cklund 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.