On the propagation of waves exhibiting both positive and negative nonlinearity

摘要: One-dimensional small-amplitude waves in which the local value of fundamental derivative changes sign are examined. The undisturbed medium is taken to be a Navier–Stokes fluid at rest and uniform with pressure density such that small. A weak shock theory developed treat inviscid motions, method multiple scales used derive nonlinear parabolic equation governing evolution weakly dissipative waves. latter compute viscous structure. New phenomena interest include having an entropy jump fourth order strength, sonic conditions either upstream or downstream shock, collisions between expansion compression shocks. When media identically zero it shown ultimate decay one-signed pulse proportional negative 1/3-power propagation time.