Lie Point Symmetries and Exact Solutions of the Coupled Volterra System

The coupled Volterra system, an integrable discrete form of a coupled Korteweg-de Vries (KdV) system applied widely in fluids, Bose-Einstein condensation and atmospheric dynamics, is studied with the help of the Lie point symmetries. Two types of delayed differential reduction systems are derived from the coupled Volterra system by means of the symmetry reduction approach and symbolic computation. Cnoidal wave and solitary wave solutions for a delayed differential reduction system and the coupled Volterra system are proposed, respectively.