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We establish the existence of traveling wave solutions for a reaction-diffusion system based on the Lotka-Volterra differential equation model of a predator and prey interaction. The waves are of transition front type, analogous to the solutions discussed by Fisher and Kolmogorov et al. for a scalar reaction-diffusion equation. The waves discussed here are not necessarily monotone. There is a speed      c ∗  &gt; 0 {c^\ast } &gt; 0       such that for      c &gt; c ∗  c &gt; {c^\ast }       there is a traveling wave moving with speed      c c      . The proof uses a shooting argument based on the nonequivalence of a simply connected region and a nonsimply connected region together with a Liapunov function to guarantee the existence of the traveling wave solution. The traveling wave solution is equivalent to a heteroclinic orbit in      4 4      -dimensional phase space.

Traveling wave solutions of diffusive Lotka-Volterra equations: a heteroclinic connection in 𝑅⁴