The nonlinear Klein-Gordon (KG) equation, ∂ t t u − Δ u + u = | u | p − 1 u , ( t , x ) ∈ R × R d is shown in the present paper to possess the solitary-wave solutions in the form of e i ω t ϕ ω , c → ( x − c → t ) with the parameters ω and c → ∈ R d satisfying | ω | < 1 − | c → | 2 and | c → | < 1 . By employing a new localized virial identity combined with the coercivity and modulation argument, it is demonstrated here that there exists a critical frequency ω ⁎ ( | c → | ) such that these localized solitary waves, when co...
