New types of wave solutions to the general nonlinear Klein-Gordon equation (Q1975768)

The author defines new types of wave solutions (namely, many-component solutions \(q_k\)) and introduces an unbounded solution. Exact wave solutions to the nonlinear Klein-Gordon equation for three different potentials are presented. The many-component functions \(q_n\) are instrumental in solving the wave equations that describe the elementary quantum-field models. Necessary and sufficient conditions for the existence of wave solutions to a quasilinear evolution equation are formulated.