An Elementary Proof Of The Existence Of Monotone Traveling Waves Solutions In A Generalized Klein-Gordon Equation

We analyze the existence and uniqueness of monotone traveling wavefront for a generalized nonlinear Klein-Gordon modelpartial derivative(2)phi/partial derivative t(2) - (p + (partial derivative phi/partial derivative x)(2)) partial derivative(2)phi/partial derivative x(2) + V'(phi) = 0,using classical arguments of ordinary differential equations, with V(x) a potentials family containing the phi-four potential V(x) = M-0(1 - x(2))(2) and the sine-Gordon-type potential V(x) = (1/2)(1 + cos(pi x)). Also for these specific potentials, we give estimations of their monotone kink and anti-kink solutions.