Context. Vertically hydrostatic protoplanetary disk models are based on the assumption that the main heating source, stellar irradiation, does not vary much with time. However, it is known that accreting young stars are variable sources of radiation. This is particularly evident for outbursting sources such as EX Lupi and FU Orionis stars.

Aims. We investigate how such outbursts affect the vertical structure of the outer regions of the protoplanetary disk, in particular their appearance in scattered light at optical and near-infrared wavelengths.

Methods. We employ the 3D FARGOCA radiation-hydrodynamics code, in polar coordinates, to compute the time-dependent behavior of the axisymmetric disk structure. The temperature is computed self-consistently and time-dependently from the irradiation flux using a two-stage radiative transfer method: first the direct illumination is computed; then the diffuse radiation is treated with the flux-limited diffusion method. The outbursting inner disk region is not included explicitly. Instead, its luminosity is added to the stellar luminosity and is thus included in the irradiation of the outer disk regions. For time snapshots of interest we insert the density structure into the RADMC-3D radiative transfer code and compute the appearance of the disk at optical/near-infrared wavelengths, where we observe stellar light that is scattered off the surface of the disk.

Results. We find that, depending on the amplitude of the outbursts, the vertical structure of the disk can become highly dynamic, featuring circular surface waves of considerable amplitude. These "hills" and "valleys" on the disk's surface show up in the scattered light images as bright and dark concentric rings. Initially these rings are small and act as standing waves, but they subsequently lead to outward propagating waves, like the waves produced by a stone thrown into a pond. These waves continue long after the actual outburst has died out.

Conclusions. Single, periodic, or quasiperiodic outbursts of the innermost regions of protoplanetary disks will necessarily lead to wavy structures on the surface of these disks at all radii. We propose that some of the multi-ringed structures seen in optical/infrared images of several protoplanetary disks may have their origin in outbursts that occurred decades or centuries ago. However, the multiple rings seen at (sub-)millimeter wavelengths in HL Tau and several other disks are not expected to be related to such waves.