There is no equivalent. Photoshop cost big money and nothing in Linux does.
:)

The GIMP has many Photoshop features, but is not equivalent. It is good
enough for the average user, but pros will find it lacking. The interface
puts some people off, but you can get a PPA for the latest beta that
provides a single window mode. Krita is good and so is Digikam. They are
more equivalent to Elements than Photoshop itself. It all depends on what
you are looking for and your level of expertise. Many who use Photoshop do
not pay for it and do not use its powerful features.

There are even more powerful applications used by studios and high end
graphics pros, such as Blender and Cinepaint. There are many specialty
applications such as Povray for Raytracing, Luminance HDR and RADIANCE
Lighting Simulation and Rendering System. There is no shortage of tools,
just not one killer app for all things.