It's understandable why Bootstrap doesn't bind the "enter" key to the button. Apart from the fact that you might not want that behaviour, you might also have multiple buttons within a single input group, and there would be no way to tell which button should be clicked.
A little bit of jQuery will tidy your code up nicely:
$(document).on("keypress", ".input-group:has(input:input, span.input-group-btn:has(div.btn)) input:input", function(e){
if (e.which == 13){
$(this).closest(".input-group").find("div.btn").click();
}
});
Boostrap btn addon clickOnEnter - JSFiddle[
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