A one-soliton solution of the ZK(m,n,k)ZK(m,n,k) equation with generalized evolution and time-dependent coefficients

We consider a nonlinear dispersive Zakharov–Kuznetsov (for short, ZK(m,n,k)ZK(m,n,k)) equation. This equation governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. A special form of this model with time-dependent coefficients of the nonlinear terms as well as the nonlinear dispersion terms is studied. Further, there are time-dependent linear attenuation and generalized evolution terms. The solitary wave ansatz is used to carry out the integration and an exact one-soliton solution is obtained. The parameters of the soliton envelope (amplitude, widths, velocity) are explicitly calculated in the course of the derivation of the exact solution, as functions of the varying model coefficients. The constraint relation between these time-dependent coefficients for the one-soliton solution to exist is established.