Applications of Bell-polynomial scheme in constructing the conversation laws of the nonlinear evolution equations admittingtwo-field bilinear forms

Li Min; Liu Chang-Jing

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Applications of Bell-polynomial scheme in constructing the conversation laws of the nonlinear evolution equations admittingtwo-field bilinear forms

Li Min 1 *, Liu Chang-Jing 2

1. Department of Mathematics and Physics, North China Electric Power University, Beijing 102206

2. College of Science, China University of Petroleum, Beijing 102249

*Correspondence author

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Funding: Fundamental Research Funds ofthe Central Universities （No.Project Nos. 2014QN30 and 2014ZZD10）, PostdoctoralScience Foundation of China （No.2013M540907）

Opened online:19 May 2015

Accepted by: none

Citation: Li Min, Liu Chang-Jing.Applications of Bell-polynomial scheme in constructing the conversation laws of the nonlinear evolution equations admittingtwo-field bilinear forms[OL]. [19 May 2015] http://en.paper.edu.cn/en_releasepaper/content/4642862

In this paper, the Bell-polynomial scheme is applied toobtain the infinite conservation laws for the nonlinear evolutionequations (NLEEs) admitting two-field bilinear forms.Bell-polynomial scheme has been used to obtain certain bilinearB"{a}cklund transformations (BTs), Lax pairs and infiniteconservation laws for the NLEEs with one-field bilinear forms. Basedon the two-field bilinear forms and four-field bilinear BTs in thebinary-Bell-polynominal form, the infinite conversation laws for avariable-coefficient modified Korteweg-de Vries equation arising influid and plasma physics as well as the Boussinesq-Burgers equationsfor the shallow water waves are construed systematically. Suchprocedure can be applied to other NLEEs admitting two-field bilinearforms.

Keywords:Bell polynomial; Infinite conservation law; Two-fieldHirota system

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