Question: Can H+ ions exist by themselves?  Edit

Answer: Electrolysis of the Concentrated solution of Hydrochloric Acid with Carbon Electrode. As the solution contains water so from there we will get small concentration of H+ ion and OH- ions.

AT CATHODE:
Low concentration of Hydrogen cation and concentrated Hydrogen cation will Migrate to the Cathode,Since both have Hydrogen cation, Hydrogen cation will Discharge at Cathode, Hydrogen gas formed as the product which the bubble of Hydrogen gas observed to go away from Cathode.
2H+ + 2e H2

AT ANODE:
Low concentration of hydroxil anion and concentrated Chloride anion will Migrate to the anode,Since Chloride anion are concentrated than hydroxil anion it will Charged at Anode, And Chlorine gas formed as the product which the bubble of Chlorine gas observed to go away from anode.
2Cl- (aq) - 2e Cl2 (g)


The overall equation for the reaction in the cell.
2H+ + 2Cl- (aq) Cl2 (g) + H2 (g)  Edit