Abstract
It is shown that the coupled Volterra system governed by two-coupled nonlinear partial differential–difference equations (PDΔEs) has many integrability properties such as Lax representation, infinitely many generalized (nonpoint) symmetries and polynomial conserved densities, and a recursion operator. A systematic investigation on the continuous point symmetries of the coupled Volterra system shows that it admits a three dimensional nilpotent Lie algebra. By exploiting the obtained continuous point symmetries a similarity reduction is obtained.
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