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This paper deals with the exact solutions of a nonlinear coupled coupled waveequation. The (G'/G)-expansion method has been applied to derive kink solutionsand singular wave solutions. The restrictions on the coefficients of thegoverning equations have also been investigated. Solitary wave solutions havealso been derived for this system of equations using Weierstrass ellipticfunction method.

(G'/G)-Expansion Method and Weierstrass Elliptic Function Method Applied to Coupled Wave Equation