We consider here the class of fully-nonlinear symmetry-integrable third-order evolution equations in 1+1 dimensions that were proposed recently in the journal Open Communications in Nonlinear Mathematical Physics, vol. 2, 216--228 (2022). In particular, we report all zero-order and higher-order potentialisations for this class of equations using their integrating factors (or multipliers) up to order four. Chains of connecting evolution equations are also obtained by multi-potentialisations.

Comment: 34 pages

• 35B06 - Symmetries, invariants, etc. in context of PDEs
• 35G25 - Initial value problems for nonlinear higher-order PDEs
• 37K10 - Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)