We consider acoustic wave propagation in a model of a deep ocean acoustic waveguide with a periodic range-dependence. Formally, the wave field is described by the Schrödinger equation with a time-dependent Hamiltonian. Using methods borrowed from the quantum chaos theory it is shown that in the driven system under consideration there exists a "scarring" effect similar to that observed in autonomous quantum systems.It is well-known in the theory of quantum chaos that classical periodic orbits, to a significant extent, determine both the distribution of energy levels and structures of eigenfunctions [1,2,3]. In particular, for some eigenfunctions, the amplitudes are high in the vicinity of unstable periodic orbits and low elsewhere. This phenomenon, first discovered in a quantum billiard, is called the scarring [4]. It has been established that the scarring is a common property for many autonomous chaotic systems [3,5,6]. The description of scarring is related to the problem of construction of eigenfunctions on the basis of purely semiclassical calculations [7,8,9,10,11,12].It is also well-known that so different physical problems as quantum particle dynamics and wave propagation in nonuniform media in the narrow beam approximation are described by the same parabolic (or Shrödinger) equation. One of the most intriguing object is the underwater acoustic (UWA) and the long range sound propagation in the ocean [13,14,15]. Application of methods of quantum chaos to the wave chaos proves to be efficient in many publications [16,17,18,19,20]. The goal of this paper is to extend this analogy between quantum and wave chaos and to present simulations that demonstrate the phenomenon of scarring in a nonautonomous Hamiltonian system with 1.5 degrees of freedom related to the UWA. We consider a simplified case of wave propagation in a two dimensional range-dependent model of hydroacoustic waveguide that has been used to study wave and ray chaos at long range sound propagation in the ocean [21,22,23,24,25]. Formally, the simplified model of ray propagation is equivalent to a nonlinear oscillator perturbed by a periodic force, while the corresponding parabolic equation is equivalent to the Shrödinger equation for the oscillator.Consider a two-dimensional UWA waveguide with the sound speed c as a function of depth, z, and range, r. In the parabolic equation approximation (valid under assumptions that waves propagate at small grazing angles) the monochromatic wave field u at a carrier frequency f obeys the parabolic equation [26,27] i k ∂u ∂r =Ĥu,Ĥ = − 1 2k 2where U (r, z) = 1 −c 2 /c 2 (r, z) /2. Herec and k = 2πf /c are a reference sound speed and a reference wavenumber, respectively. Equation (1) formally coincides with the time-dependent Schrödinger equation. In this analogy r plays a role of time,Ĥ is the Hamiltonian operator, U (r, z) is the potential, and k −1 associates with the Planck constant. The ray paths are determined by the standard Hamilton equations dp/dt = −∂H/∂z and dz/dr = ∂H/∂p with the Hamiltonian H = p 2 /2...