Numeric-Analytical Study of the Breather Type Solution on the Correctness Boundary

Asymptotics when t →∞ for the Cauchy problem solution of the equation Utt = Uxx + i2Uttx + Uttxx with discontinuous initial data are proved. The found asymptotic formulae are in a good agreement with results of numerical experiments. Stability of the numerical methods used is studied as well. At the beginning we review other results in studying nonstandard linear equations arising in averaging equations describing wave propagation in periodic stratified media.

wave propagation in periodic stratified media, nonstandard linear differential equations, Cauchy problem with discontinuous initial data, asymptotics at large t, finite difference method, the matix stepwise pursuit method, stability, system of analytical computations REDUCE