According to TeamDynamix on their portal (link, login required), the following operators are available for Full Search (what the search field in the top-right corner of the Client Portal and Knowledge Base uses):
+: Requires that both terms are included in the results. For example, cats + dogs will find results including both cats and dogs. As the AND operator is the default search operator, the previous example would be equivalent to searching for cats dogs.
-: Requires that the term after - is not included in the results. For example, cats -dogs will find results including cats and exclude all results that include dogs.
|: Allows results where either term is included. For example, cats | dogs will find results with either term.
"": Requires that the exact phrase is included in the results. For example "cats and dogs" will search for results including the exact phrase "cats and dogs".
- This is the only operator available when using the Search tab in the Knowledge Base
#: Searches for a tag, in areas that support tags. For example, #animals will search for articles that are tagged with the animals tag.
Additional Info
For information on how Full Search searches are prioritized, see this article (link).