Exact Analytic N-Soliton-Like Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg--de Vries Model from Plasmas and Fluid Dynamics

Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg--de Vries (vcKdV) model is investigated. The bilinear form and analytic N-soliton-like solution for such a model are derived by the Hirota method and Wronskian technique. Additionally, the bilinear auto-Backlund transformation between (N-1)-soliton-like and N-soliton-like solutions is verified.