Zero Curvature and generalization of Painlev\'e equation from AKNS/Lund-Regge model

We explain the relation between the mixed mKdV/sinh-Gordon model and the Kudryashov’s equation. Then, we use the mixed AKNS/Lund-Regge model to find a system of ODEs which is candidate to define a new transcendental function. We also applied the perturbative Painlev'e test and presented the local representation for the solution of the system.