Painlevé property, auto-Bäcklund transformation and analytic solutions of a variable-coefficient modified Korteweg–de Vries model in a hot magnetized dusty plasma with charge fluctuations

Under investigation in this paper is a variable-coefficient modified Korteweg–de Vries (vc-mKdV) model in a hot magnetized dusty plasma with charge fluctuations. With symbolic computation and bilinear method, Painlevé property is studied, auto-Bäcklund transformation is constructed, while soliton and other analytic solutions are obtained. Furthermore, influence of the coefficients on the dust-ion-acoustic (DIA) solitary wave propagation is investigated based on the soliton solution, which can be concluded as follows: (i) Amplitude of the DIA solitary wave is proportional to the square of the ratio of the coefficients of the dispersive to nonlinear terms; (ii) Velocity of the DIA solitary wave is controlled by the coefficients of the dispersive and dissipative terms; (iii) Propagation trajectory of the DIA solitary wave depends on the function forms of the coefficients of the dispersive, nonlinear and dissipative terms.