In this work, the exact solutions for combined KdV-mKdV generalized equation as a linear superposition of Jacobi elliptic functions, $c_n(\xi,m)$, $d_n(\xi,m)$. When $m$ is set to one, the solution matches with well-known hyperbolic solutions of generalized combined KdV-mKdV equation. Similar solution is also derived for the case for time dependent co-efficient. In the latter case the velocity term become time dependent.
Categories: math-ph math.MP nlin.SI