Integrability of two-component systems of partial differential equations

This thesis is devoted to the classification of integrable two-component polynomial homogeneous systems of equations. In the framework of the perturbative symmetry approach we derive necessary integrability conditions for such systems. We then classify integrable two-component polynomial homogeneous systems of order 3 and 5. In the Chapter 5 using the Drinfel’d–Sokolov approach we derive Lax representations for the systems obtained in the result of classification.