Plural or singular for a multi-authored paper
This is a special case of a more general problem about 'plural' names for specific organisations/groups, which often comes up (and is different in the UK and US, to complicate things) - for example, https://english.stackexchange.com/questions/138238/are-vs-is-for-proper-nouns-which-sound-plural-such-as-band-names 

Generally speaking, either is legitimate - it depends in part whether you think of "Jackson and Kim" as the name of a single entity, the paper, or as referring to two individual researchers who happen to be mentioned together. You can also avoid this entirely by using the past tense - "Jackson and Kim (2014) showed that..." is the same whether you think of J&amp;K as one entity or two. (Ditto for "found", "proved", "refuted", etc). This would be my personal preference.

Ultimately, though, all questions of style in academic writing can be answered with "have a look at what other papers in the field use; if you're thinking about a specific journal, have a look at what's common there." If they all use "show" for multiple authors, you probably want to use "show"