We consider traveling wave solutions of the reaction diffusion equation with quintic nonlinearities uₜ=uₓₓ+{μ}u(1-u)(1+{α}u+{β}u²+{γ}u³). If the parameters {α}, {β}, and {γ} obey a special relation, then the criterion for the existence of a strong heteroclinic connection can be expressed in terms of two of these parameters. If an additional restriction is imposed, explicit front solutions can be obtained. The approach used can be extended to polynomials whose highest degree is odd.
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Benguria et al. (1994) studied this question.
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