Supratim Das, Dibyendu Ghosh, AKNS Formalism and Exact Solutions of KdV and Modified KdV Equations with Variable-Coefficients, IJARM Volume 6, International Journal of Advanced Research in Mathematics (Volume 6)
    We apply the AKNS hierarchy to derive the generalized KdV equation andthe generalized modified KdV equation with variable-coefficients. We system-atically derive new exact solutions for them. The solutions turn out to beexpressible in terms of doubly-periodic Jacobian elliptic functions.
    AKNS Scheme, Homogeneous Balancing Method, Jacobian Elliptic Function, Modified KdV Equation, Variable-Coefficient KdV Equation