Integrability study on a generalized (2+1)-dimensional variable-coefficient Gardner model with symbolic computation
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. Painleve integrability conditions are derived among the coefficient functions, which reduce all the coefficient functions to be proportional only to {gamma}(t), the coefficient of the cubic nonlinear term u{sup 2}u{sub x}. Then, an independent transformation of the variable t transforms the reduced {gamma}(t)-dependent equation into a constant-coefficient integrable one. Painleve test shows that this is the only case when our original generalized (2+1)-dimensional variable-coefficient Gardner model is integrable.