Abstract
We construct nonlinear integrable couplings of the fifth-order nonlinear integrable Sawada-Kotera (SK) equation and Lax equation. We use the algebra of coupled scalars to construct the two classes of couplings. We study the constructed couplings by using the simplified Hirota's method. We show that these classes of couplings possess multiple soliton solutions the same as the multiple soliton solutions of the SK and the Lax equations, with one change in the sign of the transformation used. This change of signs exhibits soliton solution then anti-soliton solution, consecutively.