Existence and uniqueness of traveling wave front of a nonlinear singularly perturbed system of reaction–diffusion equations with a Heaviside step function

The main purpose of this paper is to show the existence and uniqueness of a traveling wave front ( U , W ) = ( U ( x + v ( ε ) t ) , W ( x + v ( ε ) t ) ) of the following nonlinear singularly perturbed system of reaction–diffusion equations with a Heaviside step function { ∂ u ∂ t = ∂ 2 u ∂ x 2 + 2 ( H ( u − θ ) − u ) − w , ∂ w ∂ t = ∂ 2 w ∂ x 2 + ε ( u − w ) .