Bell-polynomial approach applied to the seventh-order Sawada–Kotera–Ito equation

摘要

In this paper, the Bell-polynomial approach is extended to the seventh-order Sawada–Kotera–Ito equation which is regarded as a higher-order integrable one in the Korteweg-de Vries hierarchy. Through several combinations of the constructed Bell polynomials, the bilinear form with an auxiliary independent variable introduced, Bäcklund transformation, Lax pair and infinite conservation laws for such an equation are derived by means of symbolic computation.