On the Solution of the Generalized Wave and Generalized Sine‐Gordon Equations

The generalized wave equation and generalized sine‐Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two‐dimensional versions. In this paper we associate a system of linear differential equations with these equations and show how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial‐boundary‐value problem is solved for these equations.