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
 
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