Classification of qt=P(x, t, q, qx, qxx)

The classification of q_t = P ( x ,  t ,  q ,  q_x ,  q_xx ) is given by using linearization. Two types of integrable equations which are generalizations of the integrable equations of Fokas and Svinolupov are given. Results are compared with Fokas's symmetry and the Mikhailov–Shabat–Sokolov formal symmetry approaches.