var str = 'тест';
    $.ajax({
       url: 'http://' + window.location.host + '/search/test',
       type : 'GET',
       data: {
              str: str
        },
       dataType: "json",
       success: function(res){
        console.log(res);
      }
    });

var str = 'тест';
    $.ajax({
       url: 'http://' + window.location.host + '/search/test?str=' + str,
       type : 'GET',
       dataType: "json",
       success: function(res){
        console.log(res);
      }
    });