Solitonic propagation and interaction for a generalized variable-coefficient forced Korteweg-de Vries equation in fluids

Under investigation is a generalized variable-coefficient forced Korteweg-de Vries equation in fluids and other fields. From the bilinear form of such equation, the N-soliton solution and a type of analytic solution are constructed with symbolic computation. Analytic analysis indicates that: (1) dispersive and dissipative coefficients affect the solitonic velocity; (2) external-force term affects the solitonic velocity and background; (3) line-damping coefficient and some parameters affect the solitonic velocity, background, and amplitude. Solitonic propagation and interaction can be regarded as the combination of the effects of various variable coefficients. According to a constraint among the nonlinear, dispersive, and line-damping coefficients in this paper, the possible applications of our results in the real world are also discussed in three aspects, i.e., solution with the constraint, solution without the constraint, and approximate solution.