A family of nonlinear Klein–Gordon equations and their solutions

Abstract

Various forms of the nonlinear Klein–Gordon equation are seen to have exact, solitonlike solutions when separation of variables is postulated. The family for which these exact solutions are found includes the sine-Gordon equation as a special case. An interesting conclusion obtained is that both the soliton–antisoliton and breather solutions, hitherto known for the sine-Gordon equations result from a broader class of Klein–Gordon equations. The method can be extended to other equations.