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Applications of Bell-polynomial scheme in constructing the conversation laws of the nonlinear evolution equations admitting two-field bilinear forms. (English) Zbl 1394.35422
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
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