Interaction of nonlinear waves in inhomogeneous media (Q1916590)

The author develops ideas of [the author and \textit{E. A. Sagomonyan}, Mosc. Univ. Mech. Bull. 44, No. 2, 17-20 (1989); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 2, 87-89 (1989; Zbl 0721.73006) and Math. Notes 50, No. 6, 1260-1263 (1991); translation from Mat. Zametki 50, No. 6, 66-70 (1991; Zbl 0778.73012)] on the possibility of factorizing a nonlinear wave equation. He considers application of factorization ``with respect to solutions'' to asymptotic description of a short pulse of finite amplitude that is propagating in an inhomogeneous perturbed region and discusses a special case in which one wave equation can be integrated in quadratures.