So as you can see I am trying to recreate the added picture using wave texture node and I want only the red color to emit light. So that to do? and what should be the node set up?
If you want the red part to emit light, use the black and white component from your Wave Texture as the Mix Factor Between a red Emission Shader and whatever you want the rest to be (I left it as a default principled BSDF with a black BaseColor, but you can use whatever you want.)