A FAMILY OF NONLINEAR KLEIN-GORDON EQUATIONS AND THEIR SOLUTIONS

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.