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Problem statement: To obtain new exact traveling wave soliton solutions for the threewave&#13; interaction equation in a dispersive medium and a non zero phase mismatch. Approach: The&#13; tanh method is usually used to find a traveling wave analytic soliton solutions for one nonlinear wave&#13; and evolution partial differential equation. Here, we generalize this method to solve a system of&#13; nonlinear evolution partial differential equations, then we use this generalization to find new family of&#13; exact traveling wave soliton solutions for the nonlinear three-wave interaction equation. Results: We&#13; were able to generalize the tanh method and apply this generalization to the (TWI) system of (PDEs).&#13; We derive a system of algebraic Eq. 28-32 and introduced some interested sets of solutions for this&#13; system, these sets of solutions leads us to write explicit analytic new family of soliton solutions for the&#13; three-wave interaction equation. Conclusion: The generalization of the tanh method is proved its&#13; efficiency in obtaining exact solutions for nonlinear evolution partial differential equations. This&#13; method also can be used similarly to obtain exact solutions for another interested nonlinear evolution&#13; system of partial differential equations

New Family of Exact Soliton Solutions for the Nonlinear Three-Wave Interaction Equations