Answer to Question #26432 in Differential Equations for sabrina delcourt

Question

If u is a solution of u_tt -c^2u_xx = 0 on -infinity < x < +infinity, t >0 for which u-->0, u_x-->0, u_t-->0 as x--> +,- infinity, then E = integral from -inf to +inf (u^2_t + c^2u^2_x)dx is constant.

Does there exist a corresponding conservative quantity E* for solutions of the equation:
u_tt - c^2u_xx - bu = 0?