<i>N</i>-soliton solutions, Bäcklund transformation and Lax pair for a generalized variable-coefficient fifth-order Korteweg–de Vries equation

Abstract

In this paper, a generalized variable-coefficient fifth-order Korteweg–de Vries equation is investigated. Based on the Hirota bilinear method and symbolic computation, the N-soliton solutions, Bäcklund transformation and Lax pair are presented. Furthermore, the characteristic-line method is applied to discuss the solitonic propagation and collision under the effects of the variable coefficients, from which the following conclusions can be derived: (i) solitonic amplitude decreases as the positive coefficient of the line-damping term increases; (ii) coefficients of the dispersive and dissipative terms determine the solitonic direction and speed by changing the sign and absolute value of the solitonic velocity; (iii) the appearances of the characteristic lines depend on the forms of the variable coefficients.