Bell-polynomial application and multi-soliton solutions for the generalized variable-coefficient Drinfeld–Sokolov–Satsuma–Hirota system in fluids and plasmas

With symbolic computation, the generalized variable-coefficient Drinfeld–Sokolov–Satsuma–Hirota (gvcDSSH) system in fluids and plasmas is investigated. Under the constraint conditions on variable coefficients obtained via the Painleve test, the binary Bell polynomials are applied to the gvcDSSH system for its bilinear forms and multi-soliton solutions. With the different damping, dispersive and dissipative coefficients given, the multi-soliton solutions of the gvcDSSH system are illustrated and discussed. (i) The interactions between/among the solitons are elastic; (ii) the damping coefficient can only affect the amplitude of one field, while it has no effect on the other; (iii) the velocity and characteristic line for each soliton can be affected by the dispersive and dissipative coefficients.