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A nonlinear wave equation that describes different nonlinear effects invarious fields of research was considered. In two particular cases, thisequation was reduced to the Sine-Gordon equation and the Born-Infeld equation.Using the slowly varying envelope approximation and the generalizedperturbative reduction method, the nonlinear wave equation was transformed tocoupled nonlinear Schrodinger equations for auxiliary functions. An explicitanalytical solution of a nonlinear wave equation in the form of a two-breathermolecule was obtained. One breather oscillated with the sum, and the other withthe difference of frequencies and wave numbers. The obtained solution coincideswith the solutions of the two-breather molecule found in a number of well-knownequations from different areas of physics. It is shown that in a particularcase of the small amplitude waves, a solution in the form of a two-breathermolecule for the nonlinear Klein-Gordon equation coincides with the vector 0\pipulse of the self-induced transparency which is presented under less stringentconditions compared to the same solution of this equation obtained earlier.

Two-component breather solution of the nonlinear wave equation