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With the aid of the symbolic computation system Mathematica, many exact solutions for the Fitzhugh-Nagumo equation and the Klein-Gordon equation with a quadratic nonlinearity are constructed by an auxiliary equation method, the so-called ( G ' /G )-expansion method, where the new and more general forms of solutions are also obtained. Periodic and solitary traveling wave solutions capable of moving in both directions are observed.

Symbolic Computation and Construction of New Exact Traveling Wave Solutions to Fitzhugh-Nagumo and Klein-Gordon Equations