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 Thursday, 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

Thursday

Time	Location	Trainer
Morning 4am-10am	Johto - Route 44	Fisherman Wilton
Teams First Battle Fisherman Wilton Goldeen Goldeen Seaking Level 26 Level 26 Level 28 Sceond Battle Fisherman Wilton Goldeen Goldeen Seaking Level 32 Level 32 Level 36 Third Battle Fisherman Wilton Goldeen Seaking Seaking Level 32 Level 36 Level 40 Fourth Battle Fisherman Wilton Seaking Seaking Seaking Level 42 Level 46 Level 63
Morning 4am-10am	Kanto - Route 26	Ace Trainer Gaven
Teams First Battle Ace Trainer Gaven Victreebel Kingler Flareon Level 32 Level 32 Level 32 Second Battle Ace Trainer Gaven Victreebel Kingler Flareon Level 34 Level 34 Level 34 Third Battle Ace Trainer Gaven Victreebel Kingler Flareon Level 38 Level 39 Level 38 Fourth Battle Ace Trainer Gaven Victreebel Kingler Flareon Level 52 Level 49 Level 50
Day 10am-8pm	Johto - Route 32	Picnicker Liz
Teams First Battle Picnicker Liz Nidoran ♀ Level 8 Second Battle Picnicker Liz Weepinbell Nidorina Level 35 Level 38 Third Battle Picnicker Liz Weepinbell Nidorino Nidoqueen Level 39 Level 38 Level 40 Fourth Battle Picnicker Liz Weepinbell Nidoqueen Nidoqueen Level 47 Level 58 Level 60
Day 10am-8pm	Kanto - Route 12	Fisherman Kyler
Teams First Battle Fisherman Kyler Magikarp Magikarp Magikarp Level 18 Level 18 Level 18 Second Battle Fisherman Kyler Magikarp Magikarp Magikarp Magikarp Level 18 Level 18 Level 18 Level 18 Third Battle Fisherman Kyler Magikarp Magikarp Magikarp Magikarp Magikarp Level 18 Level 18 Level 18 Level 18 Level 18 Fourth Battle Fisherman Kyler Magikarp Magikarp Magikarp Magikarp Magikarp Magikarp Level 18 Level 18 Level 18 Level 18 Level 18 Level 18
Night 8pm-5am	Johto - Route 38	Lass Dana
Teams First Battle Lass Dana Flaaffy Psyduck Level 19 Level 19 Second Battle Lass Dana Flaaffy Golduck Level 32 Level 31 Third Battle Lass Dana Golduck Ampharos Level 36 Level 38 Fourth Battle Lass Dana Golduck Ampharos Level 51 Level 54
Night 8pm-5am	Kanto - Route 15	Teacher Hillary
Teams First Battle Teacher Hillary Sunkern Aipom Level 41 Level 31 Second Battle Teacher Hillary Ambipom Sunflora Level 43 Level 43 Third Battle Teacher Hillary Ambipom Sunflora Level 49 Level 49 Fourth Battle Teacher Hillary Ambipom Sunflora Level 55 Level 55