Tears and saliva are both very acidic and that could be the reason that the fur is turning brown.
There are a lot of different whiteners that you can buy over the counter. Your vet can probably recommend a good one but you probably benefit from checking with your groomer first. They deal with this problem on a daily basis so have a broader knowledge basis.
If she is licking herself a lot, you may want to have her checked and see if allergies are a problem.
Another treatment for this is giving your dog bottled or distilled water instead of tap water. Many breeders of white colored dogs swear that 1/2 tablet of tums, 2 times daily works wonders OR teaspoon of white cider vinegar added to drinking water. (it changes the ph in the tears.) Check with your vet before trying this one because I have never used it myself.
Tetracycline is the drug of choice for this common tear problem with the breed and is readily available for an adult dog from your veterinarian, (it cannot be given to puppies or pregnant bitches as it will stain juvienile teeth).
Let me know if you have more questions!
Good luck!