DALLAS — After four decades of expanding to all corners of the lower 48 states, Southwest Airlines began flying into new territory Tuesday — Jamaica, the Bahamas and Aruba.Southwest is taking over routes flown by AirTran Airways, which it bought in 2011. The company plans to eliminate the AirTran brand by year’s end. Southwest Flight 1804 left Baltimore-Washington Airport on Tuesday morning for the airline’s first overseas flight — to Oranjestad, Aruba. After the first three international destinations, it will add service next month to Cancun and Los Cabos in Mexico and will start flying to Mexico City and Punta Cana, Dominican Republic, in November. By late this year, Southwest will operate the flights from nine U.S. cities, according to a route map on its website. Still, its foreign footprint will be tiny compared with rivals American, United and Delta, which fly to Europe, Asia and South America. Southwest’s direct flights from its home base at Dallas Love Field are restricted to several nearby states by the Wright Amendment. While Southwest will be expanding long-haul flights from Love Field in October when the Wright Amendment expires, international flights from Love will still be prohibited.Southwest carries more passengers within the U.S. than any other airline, but only about 1 percent of its passenger-carrying capacity is on international routes. That might not change much. CEO Gary Kelly recently said that international will be “a relatively modest component” of the airline’s route system for several years. Still, the international flying, plus domestic expansion in New York, Washington and Dallas, is important as Southwest tries to regain momentum. In recent years, it has dealt with high fuel prices, a tepid economy, and tougher competition from both old rivals and newcomers such as JetBlue and Spirit. Southwest’s traffic — the number of miles that passengers fly — grew by double-digit percentages from 2004 through 2006. It hasn’t approached that kind of growth since, except in the year that it added AirTran. Last year, traffic grew just 1.4 percent, the second-smallest gain this century.Southwest shares (ticker: LUV) moved up 87 cents to $27.73 on Tuesday after hitting an all-time high of $27.75 earlier in the session.