Order preserving contact transformations and dynamical symmetries of scalar and coupled Riccati and Abel chains

• We have developed a way to find the dynamical symmetries associated with the Riccati and Abel chains of nonlinear scalar and coupled ordinary differential equations.
• Contact transformations that linearize the Riccati and Abel chains of nonlinear scalar and coupled ordinary differential equations to the free particle equation are given.
• The dynamical symmetries associated with the Riccati and Abel chains of nonlinear scalar and coupled ordinary differential equations are derived.

We identify contact transformations which linearize the given equations in the Riccati and Abel chains of nonlinear scalar and coupled ordinary differential equations to the same order. The identified contact transformations are not of Cole-Hopf type and are new to the literature. The linearization of Abel chain of equations is also demonstrated explicitly for the first time. The contact transformations can be utilized to derive dynamical symmetries of the associated nonlinear ODEs. The wider applicability of identifying this type of contact transformations and the method of deriving dynamical symmetries by using them is illustrated through two dimensional generalizations of the Riccati and Abel chains as well.