Extended mixed AKNS-lund-regge model and its self-similarity reduction

We discuss the relation between the self-similarity reduction of the generalized mixed mKdV-sinh-Gordon model and the fourth-order equation obtained by Kudryashov in J. Phys. A: Math. Theor. 35 (2002) 93-99. Also, it is shown two particular solutions for this equation. Then, we extend the mixed AKNS-Lund-Regge model and study its self-similarity reduction. We obtain the fifth Painlevé equation as a particular case of this reduction and a fourth-order second-degree equation otherwise. The relation between a integrable model and a fourth-order second-degree equation is interesting because the general solution of this equation must have the Painlevé property due the Ablowitz, Ramani and Segur conjecture.