In previous games, to get rematches with trainers, you used the VS Seeker to see if the trainers were willing to battle. In HeartGold & SoulSilver however, the rematches are done a different way. Firstly, only a few dozen trainers in Kanto & Johto are capable of being battled again.

In order to get the rematch, you have to receive the PokéGear number from the trainer in question. Then, on a certain day, you will need to ring the trainer in question to organise a rematch. It is not guaranteed that a rematch will be discussed when you call but keep trying and you should get it. Below is a list of all the trainers, battleable on Wednesday, and their teams including their first team and each team's increase in level. Click the other days to go to their page

Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday

Wednesday

Time	Location	Trainer
Morning 4am-10am	Johto - Route 32	Fisherman Ralph
Teams First Battle Fisherman Ralph Goldeen Level 10 Second Battle Fisherman Ralph Seaking Level 40 Third Battle Fisherman Ralph Qwilfish Seaking Level 45 Level 42 Fourth Battle Fisherman Ralph Qwilfish Seaking Level 53 Level 56
Morning 4am-10am	Kanto - Route 2	Bug Catcher Doug
Teams First Battle Bug Catcher Doug Butterfree Ariados Level 39 Level 37 Second Battle Bug Catcher Doug Butterfree Ariados Level 40 Level 40 Third Battle Bug Catcher Doug Butterfree Ariados Level 47 Level 46 Fourth Battle Bug Catcher Doug Butterfree Ariados Level 52 Level 50
Day 10am-8pm	Johto - Route 36	School Kid Alan
Teams First Battle School Kid Alan Tangela Level 17 Second Battle School Kid Alan Tangela Yanma Level 32 Level 30 Third Battle School Kid Alan Xatu Tangrowth Quagsire Yanmega Level 32 Level 36 Level 32 Level 34 Fourth Battle School Kid Alan Xatu Tangrowth Quagsire Yanmega Level 47 Level 54 Level 47 Level 54
Day 10am-8pm	Kanto - Route 12	Fisherman Kyle
Teams First Battle Fisherman Kyle Goldeen Qwilfish Goldeen Level 39 Level 35 Level 39 Second Battle Fisherman Kyle Seaking Qwilfish Seaking Level 40 Level 38 Level 40 Third Battle Fisherman Kyle Seaking Qwilfish Seaking Krabby Level 43 Level 41 Level 47 Level 39 Fourth Battle Fisherman Kyle Seaking Qwilfish Seaking Kingler Level 48 Level 49 Level 52 Level 51
Night 8pm-5am	Johto - Shining Lighthouse - 2F	Sailor Huey
Teams First Battle Sailor Huey Poliwag Poliwhirl Level 18 Level 20 Second Battle Sailor Huey Poliwhirl Poliwhirl Level 34 Level 36 Third Battle Sailor Huey Poliwhirl Poliwrath Level 38 Level 41 Fourth Battle Sailor Huey Politoed Poliwrath Level 48 Level 52
Night 8pm-5am	Johto - Route 44	Bird Keeper Vance
Teams First Battle Bird Keeper Vance Hoothoot Pidgeotto Level 28 Level 28 Second Battle Bird Keeper Vance Hoothoot Pidgeotto Level 33 Level 32 Third Battle Bird Keeper Vance Pidgeotto Pidgeot Noctowl Level 37 Level 38 Level 42 Fourth Battle Bird Keeper Vance Pidgeot Pidgeot Noctowl Level 56 Level 44 Level 54
Night 8pm-5am	Kanto - Route 14	School Kid Torin
Teams First Battle School Kid Torin Sandslash Golbat Level 41 Level 39 Second Battle School Kid Torin Sandslash Golbat Vulpix Level 46 Level 45 Level 41 Third Battle School Kid Torin Sandslash Golbat Vulpix Level 48 Level 51 Level 48 Fourth Battle School Kid Torin Sandslash Golbat Vulpix Level 52 Level 53 Level 52