1-Soliton solution of the complex KdV equation in plasmas with power law nonlinearity and time-dependent coefficients

In this paper, the complex Korteweg–de Vries equation with power law nonlinearity is studied in presence of perturbation terms. The exact 1-soliton solution is obtained. It will be seen that the time-dependent coefficients must be simply Riemann integrable for the solitons to exist. The solitary wave ansatz is used to carry out the integration.