Supratim Das, Dibyendu Ghosh, AKNS Formalism and Exact Solutions of KdV and Modified KdV Equations with Variable-Coefficients, Volume 6, International Journal of Advanced Research in Mathematics (Volume 6)
https://www.scipress.com/IJARM.6.32
Abstract:
    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.
Keywords:
    AKNS Scheme, Homogeneous Balancing Method, Jacobian Elliptic Function, Modified KdV Equation, Variable-Coefficient KdV Equation