Abstract
This chapter discusses some discontinuous periodic solutions of an autonomous wave equation. The chapter also highlights the behavior of an autonomous nonlinear wave equation using a two-variable procedure with the help of an equation. An interesting qualitative information about this equation, such as its asymptotic behavior and the existence and stability of periodic solutions, is conveniently analyzed in terms of a certain ordinary differential equation in the slow time. A solution having a 2-periodic initial condition converges with increasing time to a time-periodic limit function of the same period. The limiting value is approximated by combinations of left- and right-traveling waves.
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