Now we have the Rur river vector, we can burn it into the DEM.
1. Open the Processing Toolbox. In the main menu go to Processing | Toolbox.
2. In the Processing Toolbox choose GRASS | Raster (r.*) | r.carve
3. In the r.carve dialogue choose the dem layer as Elevation and the Rur_river_dissolved layer as Vector layer containing stream(s). Change Stream width to 60 meters, which is 2 pixels in our case. Change Additional stream depth to 2 meters, so it will be 3 meters in total. You can play with Stream width and depth to improve the result. Check the box before No flat areas allowed in flow direction. Save the Modified elevation as burndem.tif. Uncheck the Adjusted stream points layer, we don't need that.
4. Click Run. Close the dialogue after processing.
Let's style and compare the result.
5. Copy the style from the dem layer to the burndem layer.
6. Duplicate the burndem layer and style it with the hillshade renderer.
7. Create Map themes for burndem with corresponding hillshade and another one for dem with corresponding hillshade.
8. In the main menu choose View | New Map View.
9. Dock the new map view to the right side of the screen and choose the DEM Map theme for the main map canvas and DEM burned for the right map view (Map 1).