The scattering theory for nonlinear Klein–Gordon equations has been developed by many authors (such as, Segal, Strauss, Reed, and others). This chapter aims to extend recent results of Strauss on low energy scattering. In general useful methods by which one attacks nonlinear hyperbolic problem are energy estimates, Lp–Lq (decay) estimates for linear problem, and estimates of nonlinearity in various function spaces (e.g., Sobolev spaces, Besov spaces). The methods employed in this chapter are the same. The difficulty is the suitable choice of the spaces in which solutions of Nonlinear Klein-Gordon Equation (NLKG) lie.
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