On the solitary wave solutions for nonlinear Hirota–Satsuma coupled KdV of equations

In this paper an algebraic method is devised to construct new exact wave soliton solutions for two generalized nonlinear Hirota–Satsuma coupled KdV systems of partial differential equations using symbolic software like Mathematica or Maple in terms of sn(x)−cn(x) Jacobic elliptic functions and secq−tanhq q-deformed hyperbolic functions based on the idea of the homogeneous balance method.