title: Integrability study on a generalized (2+1)-dimensional variable-coefficient Gardner model with symbolic computation.
abstract: Gardner model describes certain nonlinear elastic structures, ion-acoustic waves in plasmas, and shear flows in ocean and atmosphere. In this paper, by virtue of the computerized symbolic computation, the integrability of a generalized (2+1)-dimensional variable-coefficient Gardner model is investigated. Painlevé integrability conditions are derived among the coefficient functions, which reduce all the coefficient functions to be proportional only to γ(t), the coefficient of the cubic nonlinear term u(2)u(x). Then, an independent transformation of the variable t transforms the reduced γ(t)-dependent equation into a constant-coefficient integrable one. Painlevé test shows that this is the only case when our original generalized (2+1)-dimensional variable-coefficient Gardner model is integrable.
authors.affiliation: School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876, China. xinglv655@yahoo.com.cn
authors.forename: Xing
authors.initials: X
authors.lastname: Lü
authors.forename: Bo
authors.initials: B
authors.lastname: Tian
authors.forename: Hai-Qiang
authors.initials: HQ
authors.lastname: Zhang
authors.forename: Tao
authors.initials: T
authors.lastname: Xu
authors.forename: He
authors.initials: H
authors.lastname: Li