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(2)u(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. (C) 2010 American Institute of Physics. [doi:10.1063/1.3494154]