Abstract
A general method for the construction of the second constant of motion of third and fourth orders is given for two-dimensional systems in terms of z=q1+iq2, and z̄=q1−iq2. Correspondingly, the third- and fourth-order potential equations are obtained whose solutions directly provide the integrable systems. Using the Holt ansatz, the potential equation corresponding to the third-order invariants has been reduced to a pair of potential equations whose solutions yield a large class of integrable systems.
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