Solution of coupled nonlinear partial differential equations by decomposition (Q1913462)

The system \[ {\partial^2 u\over \partial x^2}+ {\partial^2 u\over \partial t^2}+ \alpha uv= g_1(x, t),\;{\partial^2 v\over \partial x^2}+ {\partial^2 v\over \partial t^2}+ \beta uv= g_2(x, t),\quad x_1< x< x_2,\quad t> 0 \] with uncoupled initial and boundary conditions is solved using Adomian's decomposition method.