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.
International Journal of Advanced Research in Mathematics (Volume 6)
S. Das and D. Ghosh, "AKNS Formalism and Exact Solutions of KdV and Modified KdV Equations with Variable-Coefficients", International Journal of Advanced Research in Mathematics, Vol. 6, pp. 32-41, 2016