On the integrability of systems of second order evolution equations with two components
The paper aims to develop a symmetry classification of coupled systems of two nonlinear partial differential equations of the parabolic type (with two independent variables) with nonzero linear diagonal elements and nonlinearity represented by homogeneous polynomials. The eventual objective is to identify systems that are integrable in the sense of having an infinite number of symmetries. The analysis is based on computer-assisted symbolic calulations (running in Maple) that aim to find coefficient sets that support the existence of infinite series of the symmetries. The completeness of the classification is proven. The integrable systems found in the work are cast in a form without quadratic nonlinear terms, but with cubic ones necessarily present. The paper ends with giving lists of the integrable systems, and comparison with earlier works, where some of those systems have already been found.
scientific article; zbMATH DE number 2093535
scientific article